diff --git a/CHANGES b/CHANGES
index 9bb479cb7..f4a109124 100644
--- a/CHANGES
+++ b/CHANGES
@@ -15,6 +15,7 @@ Bugs fixed
 
 * #2810: Problems with pdflatex in an Italian document
 * Use ``latex_elements.papersize`` to specify papersize of LaTeX in Makefile
+* #2988: linkcheck: retry with GET request if denied HEAD request
 
 Documentation
 -------------
diff --git a/sphinx/builders/linkcheck.py b/sphinx/builders/linkcheck.py
index 371114106..e1eeb396c 100644
--- a/sphinx/builders/linkcheck.py
+++ b/sphinx/builders/linkcheck.py
@@ -84,14 +84,12 @@ class CheckExternalLinksBuilder(Builder):
         self.good = set()
         self.broken = {}
         self.redirected = {}
+        self.headers = dict(useragent_header)
         # set a timeout for non-responding servers
         socket.setdefaulttimeout(5.0)
         # create output file
         open(path.join(self.outdir, 'output.txt'), 'w').close()
 
-        self.session = requests.Session()
-        self.session.headers = dict(useragent_header)
-
         # create queues and worker threads
         self.wqueue = queue.Queue()
         self.rqueue = queue.Queue()
@@ -129,23 +127,23 @@ class CheckExternalLinksBuilder(Builder):
                     # Read the whole document and see if #anchor exists
                     # (Anchors starting with ! are ignored since they are
                     # commonly used for dynamic pages)
-                    response = self.session.get(req_url, stream=True, **kwargs)
+                    response = requests.get(req_url, stream=True, headers=self.headers,
+                                            **kwargs)
                     found = check_anchor(response, unquote(anchor))
 
                     if not found:
                         raise Exception("Anchor '%s' not found" % anchor)
                 else:
                     try:
-                        # try a HEAD request, which should be easier on
+                        # try a HEAD request first, which should be easier on
                         # the server and the network
-                        response = self.session.head(req_url, **kwargs)
+                        response = requests.head(req_url, headers=self.headers, **kwargs)
                         response.raise_for_status()
                     except HTTPError as err:
-                        if err.response.status_code not in (403, 405):
-                            raise
-                        # retry with GET if that fails, some servers
-                        # don't like HEAD requests and reply with 403 or 405
-                        response = self.session.get(req_url, stream=True, **kwargs)
+                        # retry with GET request if that fails, some servers
+                        # don't like HEAD requests.
+                        response = requests.get(req_url, stream=True, headers=self.headers,
+                                                **kwargs)
                         response.raise_for_status()
             except HTTPError as err:
                 if err.response.status_code == 401:
diff --git a/sphinx/util/requests.py b/sphinx/util/requests.py
index 095bf33e6..9bd8f251c 100644
--- a/sphinx/util/requests.py
+++ b/sphinx/util/requests.py
@@ -39,5 +39,5 @@ except pkg_resources.UnknownExtra:
         'install requests-2.4.1+.'
     )
 
-useragent_header = [('User-agent',
+useragent_header = [('User-Agent',
                      'Mozilla/5.0 (X11; Linux x86_64; rv:25.0) Gecko/20100101 Firefox/25.0')]
diff --git a/tests/test_build.py b/tests/test_build.py
index 82569074d..27a99461b 100644
--- a/tests/test_build.py
+++ b/tests/test_build.py
@@ -66,7 +66,7 @@ def test_build_all():
         )
 
     with mock.patch('sphinx.builders.linkcheck.requests') as requests:
-        requests.Session().head = request_session_head
+        requests.head = request_session_head
 
         # note: no 'html' - if it's ok with dirhtml it's ok with html
         for buildername in ['dirhtml', 'singlehtml', 'latex', 'texinfo', 'pickle',