diff --git a/src/cryptography/hazmat/backends/openssl/encode_asn1.py b/src/cryptography/hazmat/backends/openssl/encode_asn1.py
index 0ede533..796a7dc 100644
--- a/src/cryptography/hazmat/backends/openssl/encode_asn1.py
+++ b/src/cryptography/hazmat/backends/openssl/encode_asn1.py
@@ -526,6 +526,23 @@
     return nc
 
 
+def _encode_policy_constraints(backend, policy_constraints):
+    pc = backend._lib.POLICY_CONSTRAINTS_new()
+    assert pc != backend._ffi.NULL
+    pc = backend._ffi.gc(pc, backend._lib.POLICY_CONSTRAINTS_free)
+    if policy_constraints.require_explicit_policy is not None:
+        pc.requireExplicitPolicy = _encode_asn1_int(
+            backend, policy_constraints.require_explicit_policy
+        )
+
+    if policy_constraints.inhibit_policy_mapping is not None:
+        pc.inhibitPolicyMapping = _encode_asn1_int(
+            backend, policy_constraints.inhibit_policy_mapping
+        )
+
+    return pc
+
+
 def _encode_general_subtree(backend, subtrees):
     if subtrees is None:
         return backend._ffi.NULL
@@ -556,6 +573,7 @@
     ExtensionOID.INHIBIT_ANY_POLICY: _encode_inhibit_any_policy,
     ExtensionOID.OCSP_NO_CHECK: _encode_ocsp_nocheck,
     ExtensionOID.NAME_CONSTRAINTS: _encode_name_constraints,
+    ExtensionOID.POLICY_CONSTRAINTS: _encode_policy_constraints,
 }
 
 _CRL_EXTENSION_ENCODE_HANDLERS = {
diff --git a/tests/test_x509.py b/tests/test_x509.py
index c042169..a6398bb 100644
--- a/tests/test_x509.py
+++ b/tests/test_x509.py
@@ -2225,6 +2225,54 @@
         )
         assert ext.value == x509.InhibitAnyPolicy(3)
 
+    @pytest.mark.parametrize(
+        "pc",
+        [
+            x509.PolicyConstraints(
+                require_explicit_policy=None,
+                inhibit_policy_mapping=1
+            ),
+            x509.PolicyConstraints(
+                require_explicit_policy=3,
+                inhibit_policy_mapping=1
+            ),
+            x509.PolicyConstraints(
+                require_explicit_policy=0,
+                inhibit_policy_mapping=None
+            ),
+        ]
+    )
+    @pytest.mark.requires_backend_interface(interface=RSABackend)
+    @pytest.mark.requires_backend_interface(interface=X509Backend)
+    def test_policy_constraints(self, backend, pc):
+        issuer_private_key = RSA_KEY_2048.private_key(backend)
+        subject_private_key = RSA_KEY_2048.private_key(backend)
+
+        not_valid_before = datetime.datetime(2002, 1, 1, 12, 1)
+        not_valid_after = datetime.datetime(2030, 12, 31, 8, 30)
+
+        cert = x509.CertificateBuilder().subject_name(
+            x509.Name([x509.NameAttribute(NameOID.COUNTRY_NAME, u'US')])
+        ).issuer_name(
+            x509.Name([x509.NameAttribute(NameOID.COUNTRY_NAME, u'US')])
+        ).not_valid_before(
+            not_valid_before
+        ).not_valid_after(
+            not_valid_after
+        ).public_key(
+            subject_private_key.public_key()
+        ).serial_number(
+            123
+        ).add_extension(
+            pc, critical=False
+        ).sign(issuer_private_key, hashes.SHA256(), backend)
+
+        ext = cert.extensions.get_extension_for_class(
+            x509.PolicyConstraints
+        )
+        assert ext.critical is False
+        assert ext.value == pc
+
     @pytest.mark.requires_backend_interface(interface=RSABackend)
     @pytest.mark.requires_backend_interface(interface=X509Backend)
     def test_name_constraints(self, backend):