diff --git a/CHANGES b/CHANGES
index ef1d36002..78dc38213 100644
--- a/CHANGES
+++ b/CHANGES
@@ -84,6 +84,8 @@ Features added
   of ``foo[=bar]``
 * #7582: napoleon: a type for attribute are represented like type annotation
 * #7734: napoleon: overescaped trailing underscore on attribute
+* #7247: linkcheck: Add :confval:`linkcheck_request_headers` to send custom HTTP
+  headers for specific host
 * #7683: Add ``allowed_exceptions`` parameter to ``Sphinx.emit()`` to allow
   handlers to raise specified exceptions
 * #7295: C++, parse (trailing) requires clauses.
diff --git a/doc/usage/configuration.rst b/doc/usage/configuration.rst
index bc483fa1c..cdcc2a561 100644
--- a/doc/usage/configuration.rst
+++ b/doc/usage/configuration.rst
@@ -2390,6 +2390,32 @@ Options for the linkcheck builder
 
    .. versionadded:: 1.1
 
+.. confval:: linkcheck_request_headers
+
+   A dictionary that maps baseurls to HTTP request headers.
+
+   The key is a URL base string like ``"https://sphinx-doc.org/"``.  To specify
+   headers for other hosts, ``"*"`` can be used.  It matches all hosts only when
+   the URL does not match other settings.
+
+   The value is a dictionary that maps header name to its value.
+
+   Example:
+
+   .. code-block:: python
+
+      linkcheck_request_headers = {
+          "https://sphinx-doc.org/": {
+              "Accept": "text/html",
+              "Accept-Encoding": "utf-8",
+          },
+          "*": {
+              "Accept": "text/html,application/xhtml+xml",
+          }
+      }
+
+   .. versionadded:: 3.1
+
 .. confval:: linkcheck_retries
 
    The number of times the linkcheck builder will attempt to check a URL before
diff --git a/sphinx/builders/linkcheck.py b/sphinx/builders/linkcheck.py
index 9fe689ec9..dd5317087 100644
--- a/sphinx/builders/linkcheck.py
+++ b/sphinx/builders/linkcheck.py
@@ -16,7 +16,7 @@ import threading
 from html.parser import HTMLParser
 from os import path
 from typing import Any, Dict, List, Set, Tuple
-from urllib.parse import unquote
+from urllib.parse import unquote, urlparse
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -36,6 +36,11 @@ from sphinx.util.requests import is_ssl_error
 logger = logging.getLogger(__name__)
 
 
+DEFAULT_REQUEST_HEADERS = {
+    'Accept': 'text/html,application/xhtml+xml;q=0.9,*/*;q=0.8',
+}
+
+
 class AnchorCheckParser(HTMLParser):
     """Specialized HTML parser that looks for a specific anchor."""
 
@@ -107,13 +112,25 @@ class CheckExternalLinksBuilder(Builder):
     def check_thread(self) -> None:
         kwargs = {
             'allow_redirects': True,
-            'headers': {
-                'Accept': 'text/html,application/xhtml+xml;q=0.9,*/*;q=0.8',
-            },
-        }
+        }  # type: Dict
         if self.app.config.linkcheck_timeout:
             kwargs['timeout'] = self.app.config.linkcheck_timeout
 
+        def get_request_headers() -> Dict:
+            url = urlparse(uri)
+            candidates = ["%s://%s" % (url.scheme, url.netloc),
+                          "%s://%s/" % (url.scheme, url.netloc),
+                          uri,
+                          "*"]
+
+            for u in candidates:
+                if u in self.config.linkcheck_request_headers:
+                    headers = dict(DEFAULT_REQUEST_HEADERS)
+                    headers.update(self.config.linkcheck_request_headers[u])
+                    return headers
+
+            return {}
+
         def check_uri() -> Tuple[str, str, int]:
             # split off anchor
             if '#' in uri:
@@ -139,6 +156,9 @@ class CheckExternalLinksBuilder(Builder):
             else:
                 auth_info = None
 
+            # update request headers for the URL
+            kwargs['headers'] = get_request_headers()
+
             try:
                 if anchor and self.app.config.linkcheck_anchors:
                     # Read the whole document and see if #anchor exists
@@ -337,6 +357,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
 
     app.add_config_value('linkcheck_ignore', [], None)
     app.add_config_value('linkcheck_auth', [], None)
+    app.add_config_value('linkcheck_request_headers', {}, None)
     app.add_config_value('linkcheck_retries', 1, None)
     app.add_config_value('linkcheck_timeout', None, None, [int])
     app.add_config_value('linkcheck_workers', 5, None)
diff --git a/tests/test_build_linkcheck.py b/tests/test_build_linkcheck.py
index 54bde6b68..d1fec550f 100644
--- a/tests/test_build_linkcheck.py
+++ b/tests/test_build_linkcheck.py
@@ -124,3 +124,36 @@ def test_auth(app, status, warning):
                 assert c_kwargs['auth'] == 'authinfo2'
             else:
                 assert not c_kwargs['auth']
+
+
+@pytest.mark.sphinx(
+    'linkcheck', testroot='linkcheck', freshenv=True,
+    confoverrides={'linkcheck_request_headers': {
+        "https://localhost:7777/": {
+            "Accept": "text/html",
+        },
+        "http://www.sphinx-doc.org": {  # no slash at the end
+            "Accept": "application/json",
+        },
+        "*": {
+            "X-Secret": "open sesami",
+        }
+    }})
+def test_linkcheck_request_headers(app, status, warning):
+    mock_req = mock.MagicMock()
+    mock_req.return_value = 'fake-response'
+
+    with mock.patch.multiple('requests', get=mock_req, head=mock_req):
+        app.builder.build_all()
+        for args, kwargs in mock_req.call_args_list:
+            url = args[0]
+            headers = kwargs.get('headers', {})
+            if "https://localhost:7777" in url:
+                assert headers["Accept"] == "text/html"
+            elif 'http://www.sphinx-doc.org' in url:
+                assert headers["Accept"] == "application/json"
+            elif 'https://www.google.com' in url:
+                assert headers["Accept"] == "text/html,application/xhtml+xml;q=0.9,*/*;q=0.8"
+                assert headers["X-Secret"] == "open sesami"
+            else:
+                assert headers["Accept"] == "text/html,application/xhtml+xml;q=0.9,*/*;q=0.8"