diff --git a/poetry/core/semver/helpers.py b/poetry/core/semver/helpers.py
index 7d9ca49c4..11c2dfa5d 100644
--- a/poetry/core/semver/helpers.py
+++ b/poetry/core/semver/helpers.py
@@ -130,6 +130,13 @@ def parse_single_constraint(constraint: str) -> VersionTypes:
         op = m.group(1)
         version = m.group(2)
 
+        # Technically invalid constraints like `>= 3.*` will appear
+        # here as `3.`.
+        # Pip currently supports these and to avoid breaking existing
+        # users workflows we need to support them as well. To do so,
+        # we just remove the inconsequential part.
+        version = version.rstrip(".")
+
         if version == "dev":
             version = "0.0-dev"
 
diff --git a/tests/version/test_requirements.py b/tests/version/test_requirements.py
index 0a8a9bd87..c806d0bfd 100644
--- a/tests/version/test_requirements.py
+++ b/tests/version/test_requirements.py
@@ -28,6 +28,9 @@ def assert_requirement(req, name, url=None, extras=None, constraint="*", marker=
         ("name", {"name": "name"}),
         ("foo-bar.quux_baz", {"name": "foo-bar.quux_baz"}),
         ("name>=3", {"name": "name", "constraint": ">=3"}),
+        ("name>=3.*", {"name": "name", "constraint": ">=3.0"}),
+        ("name<3.*", {"name": "name", "constraint": "<3.0"}),
+        ("name>3.5.*", {"name": "name", "constraint": ">3.5"}),
         ("name==1.0.post1", {"name": "name", "constraint": "==1.0.post1"}),
         (
             "name>=1.2.3;python_version=='2.6'",