diff --git a/scrapy/linkextractors/lxmlhtml.py b/scrapy/linkextractors/lxmlhtml.py
index dd8dcdf7c..23cbd0116 100644
--- a/scrapy/linkextractors/lxmlhtml.py
+++ b/scrapy/linkextractors/lxmlhtml.py
@@ -1,6 +1,7 @@
 """
 Link extractor based on lxml.html
 """
+import logging
 import operator
 from functools import partial
 from urllib.parse import urljoin, urlparse
@@ -23,6 +24,8 @@ from scrapy.utils.python import unique as unique_list
 from scrapy.utils.response import get_base_url
 from scrapy.utils.url import url_has_any_extension, url_is_from_any_domain
 
+logger = logging.getLogger(__name__)
+
 # from lxml/src/lxml/html/__init__.py
 XHTML_NAMESPACE = "http://www.w3.org/1999/xhtml"
 
@@ -88,7 +91,12 @@ class LxmlParserLinkExtractor:
                 url = self.process_attr(attr_val)
                 if url is None:
                     continue
-            url = safe_url_string(url, encoding=response_encoding)
+            try:
+                url = safe_url_string(url, encoding=response_encoding)
+            except ValueError:
+                logger.debug(f"Skipping extraction of link with bad URL {url!r}")
+                continue
+
             # to fix relative links after process_value
             url = urljoin(response_url, url)
             link = Link(
diff --git a/tests/test_linkextractors.py b/tests/test_linkextractors.py
index f663013ba..e1ec19601 100644
--- a/tests/test_linkextractors.py
+++ b/tests/test_linkextractors.py
@@ -2,6 +2,10 @@ import pickle
 import re
 import unittest
 
+from packaging.version import Version
+from pytest import mark
+from w3lib import __version__ as w3lib_version
+
 from scrapy.http import HtmlResponse, XmlResponse
 from scrapy.link import Link
 from scrapy.linkextractors.lxmlhtml import LxmlLinkExtractor
@@ -815,3 +819,34 @@ class LxmlLinkExtractorTestCase(Base.LinkExtractorTestCase):
 
     def test_restrict_xpaths_with_html_entities(self):
         super().test_restrict_xpaths_with_html_entities()
+
+    @mark.skipif(
+        Version(w3lib_version) < Version("2.0.0"),
+        reason=(
+            "Before w3lib 2.0.0, w3lib.url.safe_url_string would not complain "
+            "about an invalid port value."
+        ),
+    )
+    def test_skip_bad_links(self):
+        html = b"""
+        <a href="http://example.org:non-port">Why would you do this?</a>
+        <a href="http://example.org/item2.html">Good Link</a>
+        <a href="http://example.org/item3.html">Good Link 2</a>
+        """
+        response = HtmlResponse("http://example.org/index.html", body=html)
+        lx = self.extractor_cls()
+        self.assertEqual(
+            [link for link in lx.extract_links(response)],
+            [
+                Link(
+                    url="http://example.org/item2.html",
+                    text="Good Link",
+                    nofollow=False,
+                ),
+                Link(
+                    url="http://example.org/item3.html",
+                    text="Good Link 2",
+                    nofollow=False,
+                ),
+            ],
+        )
diff --git a/tox.ini b/tox.ini
index d96a278ea..06b52f3dc 100644
--- a/tox.ini
+++ b/tox.ini
@@ -101,6 +101,7 @@ install_command =
     python -I -m pip install {opts} {packages}
 
 [testenv:pinned]
+basepython = python3.7
 deps =
     {[pinned]deps}
     PyDispatcher==2.0.5