diff --git a/news/5175.bugfix b/news/5175.bugfix
new file mode 100644
index 00000000000..5072bd4c9a2
--- /dev/null
+++ b/news/5175.bugfix
@@ -0,0 +1 @@
+Fix `PackageFinder.find_all_candidates` to respect the `allow_all_prereleases` parameter
diff --git a/src/pip/_internal/index.py b/src/pip/_internal/index.py
index 876fff2213f..cd88ac4642c 100644
--- a/src/pip/_internal/index.py
+++ b/src/pip/_internal/index.py
@@ -613,10 +613,11 @@ def find_all_candidates(self, project_name):
             )
 
         # This is an intentional priority ordering
-        return (
-            file_versions + find_links_versions + page_versions +
-            dependency_versions
-        )
+        all_candidates = file_versions + find_links_versions + page_versions + dependency_versions
+        if (not self.allow_all_prereleases):
+            all_candidates = [candidate for candidate in all_candidates
+                              if not candidate.version.is_prerelease]
+        return (all_candidates)
 
     def find_requirement(self, req, upgrade):
         """Try to find a Link matching req
diff --git a/tests/unit/test_finder.py b/tests/unit/test_finder.py
index 05ebed3b560..f27bec850dc 100644
--- a/tests/unit/test_finder.py
+++ b/tests/unit/test_finder.py
@@ -463,6 +463,44 @@ def test_finder_installs_pre_releases(data):
         link = finder.find_requirement(req, False)
         assert link.url == "https://foo/bar-2.0b1.tar.gz"
 
+def test_finder_does_not_return_pre_release_candidates(data):
+    """
+    Test PackageFinder finds pre-releases if asked to.
+    """
+
+    req = install_req_from_line("bar", None)
+
+    # using a local index (that has pre & dev releases)
+    finder = PackageFinder(
+        [], [data.index_url("pre")],
+        allow_all_prereleases=False,
+        session=PipSession(),
+    )
+    for candidate in finder.find_all_candidates("bar"):
+        assert not candidate.version.is_prerelease
+
+    # using find-links
+    links = ["https://foo/bar-1.0.tar.gz", "https://foo/bar-2.0b1.tar.gz"]
+    finder = PackageFinder(
+        links, [],
+        allow_all_prereleases=False,
+        session=PipSession(),
+    )
+
+    with patch.object(finder, "_get_pages", lambda x, y: []):
+        for candidate in finder.find_all_candidates("bar"):
+            assert not candidate.version.is_prerelease
+
+    links.reverse()
+    finder = PackageFinder(
+        links, [],
+        allow_all_prereleases=True,
+        session=PipSession(),
+    )
+
+    with patch.object(finder, "_get_pages", lambda x, y: []):
+        for candidate in finder.find_all_candidates("bar"):
+            assert not candidate.version.is_prerelease
 
 def test_finder_installs_dev_releases(data):
     """
@@ -492,14 +530,14 @@ def test_finder_installs_pre_releases_with_version_spec():
 
     with patch.object(finder, "_get_pages", lambda x, y: []):
         link = finder.find_requirement(req, False)
-        assert link.url == "https://foo/bar-2.0b1.tar.gz"
+        assert link.url == "https://foo/bar-1.0.tar.gz"
 
     links.reverse()
     finder = PackageFinder(links, [], session=PipSession())
 
     with patch.object(finder, "_get_pages", lambda x, y: []):
         link = finder.find_requirement(req, False)
-        assert link.url == "https://foo/bar-2.0b1.tar.gz"
+        assert link.url == "https://foo/bar-1.0.tar.gz"
 
 
 class test_link_package_versions(object):