diff --git a/docs/changelog.rst b/docs/changelog.rst
index dc92d2de7..085fef400 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -58,6 +58,8 @@ Detailed list of changes
 
 - A new mouse action ``mouse_selection word_and_line_from_point`` to select the current word under the mouse cursor and extend to end of line (:pull:`6663`)
 
+- A new option :opt:`underline_hyperlinks` to control when hyperlinks are underlined (:iss:`6766`)
+
 - Allow using the full range of standard mouse cursor shapes when customizing the mouse cursor
 
 - macOS: When running the default shell with the login program fix :file:`~/.hushlogin` not being respected when opening windows not in the home directory (:iss:`6689`)
diff --git a/kitty/line.c b/kitty/line.c
index 930b372f2..9895a3cd8 100644
--- a/kitty/line.c
+++ b/kitty/line.c
@@ -660,6 +660,10 @@ line_set_char(Line *self, unsigned int at, uint32_t ch, unsigned int width, Curs
     }
     self->cpu_cells[at].ch = ch;
     self->cpu_cells[at].hyperlink_id = hyperlink_id;
+    if (OPT(underline_hyperlinks) == UNDERLINE_ALWAYS && hyperlink_id) {
+        g->decoration_fg = ((OPT(url_color) & COL_MASK) << 8) | 2;
+        g->attrs.decoration = OPT(url_style);
+    }
     memset(self->cpu_cells[at].cc_idx, 0, sizeof(self->cpu_cells[at].cc_idx));
 }
 
diff --git a/kitty/options/definition.py b/kitty/options/definition.py
index 309cc1833..1c39f9efc 100644
--- a/kitty/options/definition.py
+++ b/kitty/options/definition.py
@@ -486,7 +486,8 @@ opt('detect_urls', 'yes',
     long_text='''
 Detect URLs under the mouse. Detected URLs are highlighted with an underline and
 the mouse cursor becomes a hand over them. Even if this option is disabled, URLs
-are still clickable.
+are still clickable. See also the :opt:`underline_hyperlinks` option to control
+how hyperlinks (as opposed to plain text URLs) are displayed.
 '''
     )
 
@@ -510,6 +511,16 @@ When the mouse hovers over a terminal hyperlink, show the actual URL that will
 be activated when the hyperlink is clicked.
 ''')
 
+
+opt('underline_hyperlinks', 'hover', choices=('hover', 'always', 'never'),
+    ctype='underline_hyperlinks', long_text='''
+Control how hyperlinks are underlined. They can either be underlined on mouse
+``hover``, ``always`` (i.e. permanently underlined) or ``never`` which means
+that kitty will not apply any underline styling to hyperlinks.
+Uses the :opt:`url_style` and :opt:`url_color` settings for the underline style.
+''')
+
+
 opt('copy_on_select', 'no',
     option_type='copy_on_select',
     long_text='''
diff --git a/kitty/options/parse.py b/kitty/options/parse.py
index f6cb0c536..752680382 100644
--- a/kitty/options/parse.py
+++ b/kitty/options/parse.py
@@ -1308,6 +1308,14 @@ class Parser:
 
     choices_for_undercurl_style = frozenset(('thin-sparse', 'thin-dense', 'thick-sparse', 'thick-dense'))
 
+    def underline_hyperlinks(self, val: str, ans: typing.Dict[str, typing.Any]) -> None:
+        val = val.lower()
+        if val not in self.choices_for_underline_hyperlinks:
+            raise ValueError(f"The value {val} is not a valid choice for underline_hyperlinks")
+        ans["underline_hyperlinks"] = val
+
+    choices_for_underline_hyperlinks = frozenset(('hover', 'always', 'never'))
+
     def update_check_interval(self, val: str, ans: typing.Dict[str, typing.Any]) -> None:
         ans['update_check_interval'] = float(val)
 
diff --git a/kitty/options/to-c-generated.h b/kitty/options/to-c-generated.h
index bf2ca731d..4e987456c 100644
--- a/kitty/options/to-c-generated.h
+++ b/kitty/options/to-c-generated.h
@@ -291,6 +291,19 @@ convert_from_opts_show_hyperlink_targets(PyObject *py_opts, Options *opts) {
     Py_DECREF(ret);
 }
 
+static void
+convert_from_python_underline_hyperlinks(PyObject *val, Options *opts) {
+    opts->underline_hyperlinks = underline_hyperlinks(val);
+}
+
+static void
+convert_from_opts_underline_hyperlinks(PyObject *py_opts, Options *opts) {
+    PyObject *ret = PyObject_GetAttrString(py_opts, "underline_hyperlinks");
+    if (ret == NULL) return;
+    convert_from_python_underline_hyperlinks(ret, opts);
+    Py_DECREF(ret);
+}
+
 static void
 convert_from_python_select_by_word_characters(PyObject *val, Options *opts) {
     select_by_word_characters(val, opts);
@@ -1143,6 +1156,8 @@ convert_opts_from_python_opts(PyObject *py_opts, Options *opts) {
     if (PyErr_Occurred()) return false;
     convert_from_opts_show_hyperlink_targets(py_opts, opts);
     if (PyErr_Occurred()) return false;
+    convert_from_opts_underline_hyperlinks(py_opts, opts);
+    if (PyErr_Occurred()) return false;
     convert_from_opts_select_by_word_characters(py_opts, opts);
     if (PyErr_Occurred()) return false;
     convert_from_opts_select_by_word_characters_forward(py_opts, opts);
diff --git a/kitty/options/to-c.h b/kitty/options/to-c.h
index b9b0f0b0f..76608e200 100644
--- a/kitty/options/to-c.h
+++ b/kitty/options/to-c.h
@@ -57,6 +57,16 @@ window_title_in(PyObject *title_in) {
     return ALL;
 }
 
+static UnderlineHyperlinks
+underline_hyperlinks(PyObject *x) {
+    const char *in = PyUnicode_AsUTF8(x);
+    switch(in[0]) {
+        case 'a': return UNDERLINE_ALWAYS;
+        case 'n': return UNDERLINE_NEVER;
+        default : return UNDERLINE_ON_HOVER;
+    }
+}
+
 static BackgroundImageLayout
 bglayout(PyObject *layout_name) {
     const char *name = PyUnicode_AsUTF8(layout_name);
diff --git a/kitty/options/types.py b/kitty/options/types.py
index f18f0d619..720acf541 100644
--- a/kitty/options/types.py
+++ b/kitty/options/types.py
@@ -29,6 +29,7 @@ choices_for_tab_bar_style = typing.Literal['fade', 'hidden', 'powerline', 'separ
 choices_for_tab_powerline_style = typing.Literal['angled', 'round', 'slanted']
 choices_for_tab_switch_strategy = typing.Literal['last', 'left', 'previous', 'right']
 choices_for_undercurl_style = typing.Literal['thin-sparse', 'thin-dense', 'thick-sparse', 'thick-dense']
+choices_for_underline_hyperlinks = typing.Literal['hover', 'always', 'never']
 choices_for_window_logo_position = typing.Literal['top-left', 'top', 'top-right', 'left', 'center', 'right', 'bottom-left', 'bottom', 'bottom-right']
 
 option_names = (  # {{{
@@ -432,6 +433,7 @@ option_names = (  # {{{
  'text_fg_override_threshold',
  'touch_scroll_multiplier',
  'undercurl_style',
+ 'underline_hyperlinks',
  'update_check_interval',
  'url_color',
  'url_excluded_characters',
@@ -588,6 +590,7 @@ class Options:
     text_fg_override_threshold: float = 0.0
     touch_scroll_multiplier: float = 1.0
     undercurl_style: choices_for_undercurl_style = 'thin-sparse'
+    underline_hyperlinks: choices_for_underline_hyperlinks = 'hover'
     update_check_interval: float = 24.0
     url_color: Color = Color(0, 135, 189)
     url_excluded_characters: str = ''
diff --git a/kitty/screen.c b/kitty/screen.c
index 666b7403e..4ddda5104 100644
--- a/kitty/screen.c
+++ b/kitty/screen.c
@@ -2809,7 +2809,9 @@ screen_apply_selection(Screen *self, void *address, size_t size) {
     }
     self->selections.last_rendered_count = self->selections.count;
     for (size_t i = 0; i < self->url_ranges.count; i++) {
-        apply_selection(self, address, self->url_ranges.items + i, 2);
+        Selection *s = self->url_ranges.items + i;
+        if (OPT(underline_hyperlinks) == UNDERLINE_NEVER && s->is_hyperlink) continue;
+        apply_selection(self, address, s, 2);
     }
     self->url_ranges.last_rendered_count = self->url_ranges.count;
 }
@@ -3945,12 +3947,13 @@ screen_start_selection(Screen *self, index_type x, index_type y, bool in_left_ha
 }
 
 static void
-add_url_range(Screen *self, index_type start_x, index_type start_y, index_type end_x, index_type end_y) {
+add_url_range(Screen *self, index_type start_x, index_type start_y, index_type end_x, index_type end_y, bool is_hyperlink) {
 #define A(attr, val) r->attr = val;
     ensure_space_for(&self->url_ranges, items, Selection, self->url_ranges.count + 8, capacity, 8, false);
     Selection *r = self->url_ranges.items + self->url_ranges.count++;
     memset(r, 0, sizeof(Selection));
     r->last_rendered.y = INT_MAX;
+    r->is_hyperlink = is_hyperlink;
     A(start.x, start_x); A(end.x, end_x); A(start.y, start_y); A(end.y, end_y);
     A(start_scrolled_by, self->scrolled_by); A(end_scrolled_by, self->scrolled_by);
     A(start.in_left_half_of_cell, true);
@@ -3960,7 +3963,7 @@ add_url_range(Screen *self, index_type start_x, index_type start_y, index_type e
 void
 screen_mark_url(Screen *self, index_type start_x, index_type start_y, index_type end_x, index_type end_y) {
     self->url_ranges.count = 0;
-    if (start_x || start_y || end_x || end_y) add_url_range(self, start_x, start_y, end_x, end_y);
+    if (start_x || start_y || end_x || end_y) add_url_range(self, start_x, start_y, end_x, end_y, false);
 }
 
 static bool
@@ -3972,7 +3975,7 @@ mark_hyperlinks_in_line(Screen *self, Line *line, hyperlink_id_type id, index_ty
         bool has_hyperlink = line->cpu_cells[x].hyperlink_id == id;
         if (in_range) {
             if (!has_hyperlink) {
-                add_url_range(self, start, y, x - 1, y);
+                add_url_range(self, start, y, x - 1, y, true);
                 in_range = false;
                 start = 0;
             }
@@ -3983,7 +3986,7 @@ mark_hyperlinks_in_line(Screen *self, Line *line, hyperlink_id_type id, index_ty
             }
         }
     }
-    if (in_range) add_url_range(self, start, y, self->columns - 1, y);
+    if (in_range) add_url_range(self, start, y, self->columns - 1, y, true);
     return found;
 }
 
diff --git a/kitty/screen.h b/kitty/screen.h
index 5d8340eea..abfbdbbcf 100644
--- a/kitty/screen.h
+++ b/kitty/screen.h
@@ -39,7 +39,7 @@ typedef struct {
 typedef struct {
     SelectionBoundary start, end, input_start, input_current;
     unsigned int start_scrolled_by, end_scrolled_by;
-    bool rectangle_select, adjusting_start;
+    bool rectangle_select, adjusting_start, is_hyperlink;
     IterationData last_rendered;
     int sort_y, sort_x;
     struct {
diff --git a/kitty/state.h b/kitty/state.h
index 298007609..e9d57b75f 100644
--- a/kitty/state.h
+++ b/kitty/state.h
@@ -22,6 +22,7 @@ typedef struct {
 } UrlPrefix;
 
 typedef enum AdjustmentUnit { POINT = 0, PERCENT = 1, PIXEL = 2 } AdjustmentUnit;
+typedef enum UnderlineHyperlinks { UNDERLINE_ON_HOVER = 0, UNDERLINE_ALWAYS = 1, UNDERLINE_NEVER = 2 } UnderlineHyperlinks;
 
 struct MenuItem {
     const char* *location;
@@ -95,6 +96,7 @@ typedef struct {
         float val; AdjustmentUnit unit;
     } underline_position, underline_thickness, strikethrough_position, strikethrough_thickness, cell_width, cell_height, baseline;
     bool show_hyperlink_targets;
+    UnderlineHyperlinks underline_hyperlinks;
     int background_blur;
     long macos_titlebar_color;
     unsigned long wayland_titlebar_color;