diff --git a/_pytest/python.py b/_pytest/python.py
index 96eec73df..f145ca5b8 100644
--- a/_pytest/python.py
+++ b/_pytest/python.py
@@ -277,13 +277,12 @@ class PyCollector(PyobjMixin, pytest.Collector):
                 if name in seen:
                     continue
                 seen[name] = True
-                if name[0] != "_":
-                    res = self.makeitem(name, obj)
-                    if res is None:
-                        continue
-                    if not isinstance(res, list):
-                        res = [res]
-                    l.extend(res)
+                res = self.makeitem(name, obj)
+                if res is None:
+                    continue
+                if not isinstance(res, list):
+                    res = [res]
+                l.extend(res)
         l.sort(key=lambda item: item.reportinfo()[:2])
         return l
 
diff --git a/testing/python/collect.py b/testing/python/collect.py
index fc41bf738..5f1de8830 100644
--- a/testing/python/collect.py
+++ b/testing/python/collect.py
@@ -659,6 +659,28 @@ def test_customized_python_discovery(testdir):
         "*2 passed*",
     ])
 
+
+def test_customized_python_discovery_functions(testdir):
+    testdir.makeini("""
+        [pytest]
+        python_functions=_test
+    """)
+    p = testdir.makepyfile("""
+        def _test_underscore():
+            pass
+    """)
+    result = testdir.runpytest("--collectonly", "-s")
+    result.stdout.fnmatch_lines([
+        "*_test_underscore*",
+    ])
+
+    result = testdir.runpytest()
+    assert result.ret == 0
+    result.stdout.fnmatch_lines([
+        "*1 passed*",
+    ])
+
+
 def test_collector_attributes(testdir):
     testdir.makeconftest("""
         import pytest