diff --git a/test/parallel/test-crypto-dh.js b/test/parallel/test-crypto-dh.js
index abbe1abe7e53d7..3b738b7f47ec59 100644
--- a/test/parallel/test-crypto-dh.js
+++ b/test/parallel/test-crypto-dh.js
@@ -85,11 +85,15 @@ const crypto = require('crypto');
     }, wrongBlockLength);
   }
 
-  assert.throws(() => {
-    dh3.computeSecret('');
-  }, { message: common.hasOpenSSL3 ?
-    'error:02800080:Diffie-Hellman routines::invalid secret' :
-    'Supplied key is too small' });
+  {
+    const v = crypto.constants.OPENSSL_VERSION_NUMBER;
+    const hasOpenSSL3WithNewErrorMessage = (v >= 0x300000c0 && v <= 0x30100000) || (v >= 0x30100040 && v <= 0x30200000);
+    assert.throws(() => {
+      dh3.computeSecret('');
+    }, { message: common.hasOpenSSL3 && !hasOpenSSL3WithNewErrorMessage ?
+      'error:02800080:Diffie-Hellman routines::invalid secret' :
+      'Supplied key is too small' });
+  }
 }
 
 // Through a fluke of history, g=0 defaults to DH_GENERATOR (2).