diff --git a/CHANGES b/CHANGES
index bc932a7d48c..7af591708c3 100644
--- a/CHANGES
+++ b/CHANGES
@@ -27,6 +27,7 @@ Features added
 * #7902: html theme: Add a new option :confval:`globaltoc_maxdepth` to control
   the behavior of globaltoc in sidebar
 * #7840: i18n: Optimize the dependencies check on bootstrap
+* #5208: linkcheck: Support checks for local links
 * #7052: add ``:noindexentry:`` to the Python, C, C++, and Javascript domains.
   Update the documentation to better reflect the relationship between this option
   and the ``:noindex:`` option.
diff --git a/sphinx/builders/linkcheck.py b/sphinx/builders/linkcheck.py
index dd531708729..ef8f9d90222 100644
--- a/sphinx/builders/linkcheck.py
+++ b/sphinx/builders/linkcheck.py
@@ -35,6 +35,8 @@
 
 logger = logging.getLogger(__name__)
 
+uri_re = re.compile('[a-z]+://')
+
 
 DEFAULT_REQUEST_HEADERS = {
     'Accept': 'text/html,application/xhtml+xml;q=0.9,*/*;q=0.8',
@@ -210,10 +212,21 @@ def check_uri() -> Tuple[str, str, int]:
 
         def check() -> Tuple[str, str, int]:
             # check for various conditions without bothering the network
-            if len(uri) == 0 or uri.startswith(('#', 'mailto:', 'ftp:')):
+            if len(uri) == 0 or uri.startswith(('#', 'mailto:')):
                 return 'unchecked', '', 0
             elif not uri.startswith(('http:', 'https:')):
-                return 'local', '', 0
+                if uri_re.match(uri):
+                    # non supported URI schemes (ex. ftp)
+                    return 'unchecked', '', 0
+                else:
+                    if path.exists(path.join(self.srcdir, uri)):
+                        return 'working', '', 0
+                    else:
+                        for rex in self.to_ignore:
+                            if rex.match(uri):
+                                return 'ignored', '', 0
+                        else:
+                            return 'broken', '', 0
             elif uri in self.good:
                 return 'working', 'old', 0
             elif uri in self.broken:
diff --git a/tests/roots/test-linkcheck/links.txt b/tests/roots/test-linkcheck/links.txt
index fa8f11e4cf4..90759ee6369 100644
--- a/tests/roots/test-linkcheck/links.txt
+++ b/tests/roots/test-linkcheck/links.txt
@@ -11,6 +11,8 @@ Some additional anchors to exercise ignore code
 * `Example Bar invalid <https://www.google.com/#top>`_
 * `Example anchor invalid <http://www.sphinx-doc.org/en/1.7/intro.html#does-not-exist>`_
 * `Complete nonsense <https://localhost:7777/doesnotexist>`_
+* `Example valid local file <conf.py>`_
+* `Example invalid local file <path/to/notfound>`_
 
 .. image:: https://www.google.com/image.png
 .. figure:: https://www.google.com/image2.png
diff --git a/tests/test_build_linkcheck.py b/tests/test_build_linkcheck.py
index d1fec550f7b..7d85f10c53a 100644
--- a/tests/test_build_linkcheck.py
+++ b/tests/test_build_linkcheck.py
@@ -30,7 +30,9 @@ def test_defaults(app, status, warning):
     # images should fail
     assert "Not Found for url: https://www.google.com/image.png" in content
     assert "Not Found for url: https://www.google.com/image2.png" in content
-    assert len(content.splitlines()) == 5
+    # looking for local file should fail
+    assert "[broken] path/to/notfound" in content
+    assert len(content.splitlines()) == 6
 
 
 @pytest.mark.sphinx('linkcheck', testroot='linkcheck', freshenv=True)
@@ -47,8 +49,8 @@ def test_defaults_json(app, status, warning):
                  "info"]:
         assert attr in row
 
-    assert len(content.splitlines()) == 8
-    assert len(rows) == 8
+    assert len(content.splitlines()) == 10
+    assert len(rows) == 10
     # the output order of the rows is not stable
     # due to possible variance in network latency
     rowsby = {row["uri"]:row for row in rows}
@@ -69,7 +71,7 @@ def test_defaults_json(app, status, warning):
     assert dnerow['uri'] == 'https://localhost:7777/doesnotexist'
     assert rowsby['https://www.google.com/image2.png'] == {
         'filename': 'links.txt',
-        'lineno': 16,
+        'lineno': 18,
         'status': 'broken',
         'code': 0,
         'uri': 'https://www.google.com/image2.png',
@@ -92,7 +94,8 @@ def test_defaults_json(app, status, warning):
                        'https://localhost:7777/doesnotexist',
                        'http://www.sphinx-doc.org/en/1.7/intro.html#',
                        'https://www.google.com/image.png',
-                       'https://www.google.com/image2.png']
+                       'https://www.google.com/image2.png',
+                       'path/to/notfound']
                    })
 def test_anchors_ignored(app, status, warning):
     app.builder.build_all()