diff --git a/jose/jws.py b/jose/jws.py
index 27f6b79..cc6c9ff 100644
--- a/jose/jws.py
+++ b/jose/jws.py
@@ -74,6 +74,7 @@ def verify(token, key, algorithms, verify=True):
     header, payload, signing_input, signature = _load(token)
 
     if verify:
+        _validate_crit(header)
         _verify_signature(signing_input, header, signature, key, algorithms)
 
     return payload
@@ -206,6 +207,40 @@ def _load(jwt):
     return (header, payload, signing_input, signature)
 
 
+# Header parameter names that may legitimately appear in a "crit" list and
+# that this library understands. RFC 7515 forbids the standard header
+# parameters defined by RFC 7515/7518 from being listed in "crit", so this set
+# is intentionally empty: python-jose does not implement any of the optional
+# extensions (for example "b64" from RFC 7797) that "crit" is meant to flag.
+_UNDERSTOOD_CRIT_HEADERS = frozenset()
+
+
+def _validate_crit(header):
+    """Enforce RFC 7515 section 4.1.11 "crit" (Critical) header handling.
+
+    A JWS whose protected header lists a critical extension that the verifier
+    does not understand MUST be rejected (fail closed). python-jose implements
+    none of the optional "crit" extensions, so any well-formed, non-empty
+    "crit" list is unsupported. Malformed "crit" values are also rejected.
+    """
+    if "crit" not in header:
+        return
+
+    crit = header["crit"]
+
+    # Per RFC 7515, "crit" must be an array of non-empty case-sensitive strings.
+    if not isinstance(crit, list) or not crit:
+        raise JWSError("Invalid crit header: must be a non-empty list of strings")
+
+    for name in crit:
+        if not isinstance(name, str) or not name:
+            raise JWSError("Invalid crit header: must be a non-empty list of strings")
+
+    unsupported = [name for name in crit if name not in _UNDERSTOOD_CRIT_HEADERS]
+    if unsupported:
+        raise JWSError("Unsupported crit header parameter(s): %s" % ", ".join(unsupported))
+
+
 def _sig_matches_keys(keys, signing_input, signature, alg):
     for key in keys:
         if not isinstance(key, Key):
diff --git a/tests/test_jws.py b/tests/test_jws.py
index 1609b6b..54e97e5 100644
--- a/tests/test_jws.py
+++ b/tests/test_jws.py
@@ -90,6 +90,64 @@ def test_round_trip_with_different_key_types(self, key):
         assert verified_data["testkey"] == "testvalue"
 
 
+class TestCrit:
+    """RFC 7515 section 4.1.11 "crit" (Critical) header enforcement."""
+
+    def _make_token(self, secret, headers):
+        import base64
+
+        header = {"alg": "HS256", "typ": "JWT"}
+        header.update(headers)
+        header_segment = base64.urlsafe_b64encode(json.dumps(header, separators=(",", ":")).encode("utf-8")).rstrip(
+            b"="
+        )
+        claims_segment = base64.urlsafe_b64encode(b'{"a":"b"}').rstrip(b"=")
+        signing_input = header_segment + b"." + claims_segment
+
+        from jose import jwk
+
+        key = jwk.construct(secret, "HS256")
+        signature = base64.urlsafe_b64encode(key.sign(signing_input)).rstrip(b"=")
+        return (signing_input + b"." + signature).decode("utf-8")
+
+    def test_unsupported_crit_extension_is_rejected(self):
+        # A correctly signed token whose protected header declares an
+        # unsupported critical extension must fail closed (RFC 7515 4.1.11).
+        token = self._make_token(
+            "secret",
+            {"crit": ["x-custom-policy"], "x-custom-policy": "require-mfa"},
+        )
+        with pytest.raises(JWSError):
+            jws.verify(token, "secret", ["HS256"])
+
+    def test_token_without_crit_still_verifies(self):
+        token = self._make_token("secret", {})
+        assert jws.verify(token, "secret", ["HS256"]) == b'{"a":"b"}'
+
+    def test_crit_not_a_list_is_rejected(self):
+        token = self._make_token("secret", {"crit": "x-custom-policy"})
+        with pytest.raises(JWSError):
+            jws.verify(token, "secret", ["HS256"])
+
+    def test_empty_crit_list_is_rejected(self):
+        token = self._make_token("secret", {"crit": []})
+        with pytest.raises(JWSError):
+            jws.verify(token, "secret", ["HS256"])
+
+    def test_crit_with_non_string_entry_is_rejected(self):
+        token = self._make_token("secret", {"crit": ["x-custom-policy", 1]})
+        with pytest.raises(JWSError):
+            jws.verify(token, "secret", ["HS256"])
+
+    def test_crit_skipped_when_verify_disabled(self):
+        # verify=False should not enforce crit, mirroring signature skipping.
+        token = self._make_token(
+            "secret",
+            {"crit": ["x-custom-policy"], "x-custom-policy": "require-mfa"},
+        )
+        assert jws.verify(token, "secret", ["HS256"], verify=False) == b'{"a":"b"}'
+
+
 class TestJWK:
     def test_jwk(self, payload):
         key_data = "key"