diff --git a/changelogs/fragments/457-certificate_complete_chain-unsupported-algorithm.yml b/changelogs/fragments/457-certificate_complete_chain-unsupported-algorithm.yml
new file mode 100644
index 00000000..0d729b6d
--- /dev/null
+++ b/changelogs/fragments/457-certificate_complete_chain-unsupported-algorithm.yml
@@ -0,0 +1,2 @@
+bugfixes:
+  - "certificate_complete_chain - do not stop execution if an unsupported signature algorithm is encountered; warn instead (https://github.com/ansible-collections/community.crypto/pull/457)."
diff --git a/plugins/modules/certificate_complete_chain.py b/plugins/modules/certificate_complete_chain.py
index 87b1b885..e0666cfb 100644
--- a/plugins/modules/certificate_complete_chain.py
+++ b/plugins/modules/certificate_complete_chain.py
@@ -133,6 +133,7 @@ from ansible_collections.community.crypto.plugins.module_utils.crypto.pem import
 CRYPTOGRAPHY_IMP_ERR = None
 try:
     import cryptography
+    import cryptography.exceptions
     import cryptography.hazmat.backends
     import cryptography.hazmat.primitives.serialization
     import cryptography.hazmat.primitives.asymmetric.rsa
@@ -190,6 +191,9 @@ def is_parent(module, cert, potential_parent):
         return True
     except cryptography.exceptions.InvalidSignature as dummy:
         return False
+    except cryptography.exceptions.UnsupportedAlgorithm as dummy:
+        module.warn('Unsupported algorithm "{0}"'.format(cert.cert.signature_hash_algorithm))
+        return False
     except Exception as e:
         module.fail_json(msg='Unknown error on signature validation: {0}'.format(e))