diff --git a/Lib/email/utils.py b/Lib/email/utils.py
index f276303197396b..f2c28bf7f81af6 100644
--- a/Lib/email/utils.py
+++ b/Lib/email/utils.py
@@ -417,6 +417,9 @@ def decode_params(params):
         for name, continuations in rfc2231_params.items():
             value = []
             extended = False
+            if len(continuations) > 1 and any(num is None for num, *_ in continuations):
+                msg = f"Invalid RFC 2231 parameter continuation for '{name}'"
+                raise ValueError(msg)
             # Sort by number
             continuations.sort()
             # And now append all values in numerical order, converting
diff --git a/Lib/test/test_email/test_email.py b/Lib/test/test_email/test_email.py
index 65ddbabcaa1997..ac9e424fb5d494 100644
--- a/Lib/test/test_email/test_email.py
+++ b/Lib/test/test_email/test_email.py
@@ -5757,6 +5757,16 @@ def test_should_not_hang_on_invalid_ew_messages(self):
             with self.subTest(m=m):
                 msg = email.message_from_string(m)
 
+    def test_rfc2231_invalid_parameter_continuation(self):
+        # gh-125648: should raise a ValueError for invalid parameter continuation
+        m = """\
+Content-Type: application/x-foo;
+\tname*0="foo";
+\tname*="bar"
+"""
+        msg = email.message_from_string(m)
+        with self.assertRaisesRegex(ValueError, "Invalid RFC 2231 parameter continuation for 'name'"):
+            msg.get_params()
 
 # Tests to ensure that signed parts of an email are completely preserved, as
 # required by RFC1847 section 2.1.  Note that these are incomplete, because the
diff --git a/Misc/NEWS.d/next/Library/2024-10-20-21-02-53.gh-issue-125648.HnDHxg.rst b/Misc/NEWS.d/next/Library/2024-10-20-21-02-53.gh-issue-125648.HnDHxg.rst
new file mode 100644
index 00000000000000..b0fe678c717a6b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-10-20-21-02-53.gh-issue-125648.HnDHxg.rst
@@ -0,0 +1,2 @@
+Use a more descriptive error message when encountering invalid parameter
+continuations in :meth:`email.message.Message.get_params`.