diff --git a/Lib/smtplib.py b/Lib/smtplib.py
index 72093f7f8b0f2d..fd8e562a69e40f 100644
--- a/Lib/smtplib.py
+++ b/Lib/smtplib.py
@@ -148,9 +148,10 @@ def quoteaddr(addrstring):
     """
     displayname, addr = email.utils.parseaddr(addrstring)
     if (displayname, addr) == ('', ''):
-        # parseaddr couldn't parse it, use it as is and hope for the best.
+        # parseaddr couldn't parse it, wrap it in angle brackets.
         if addrstring.strip().startswith('<'):
-            return addrstring
+            if addrstring.strip().endswith('>'):
+                return addrstring
         return "<%s>" % addrstring
     return "<%s>" % addr
 
diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index b8aac8c20202a2..78239403814ae1 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -77,6 +77,21 @@ def testQuoteData(self):
         expected = "abc\r\n..jkl\r\nfoo\r\n...blue"
         self.assertEqual(expected, smtplib.quotedata(teststr))
 
+    def testQuoteAddr(self):
+        self.assertEqual(smtplib.quoteaddr('user@example.com'),
+                         '<user@example.com>')
+        self.assertEqual(smtplib.quoteaddr('<user@example.com>'),
+                         '<user@example.com>')
+        self.assertEqual(smtplib.quoteaddr(''), '<>')
+
+    def testQuoteAddrMalformedAngleBracket(self):
+        result = smtplib.quoteaddr('<')
+        self.assertTrue(result.startswith('<') and result.endswith('>'), result)
+        result = smtplib.quoteaddr('< ')
+        self.assertTrue(result.startswith('<') and result.endswith('>'), result)
+        result = smtplib.quoteaddr('<user@example.com')
+        self.assertTrue(result.startswith('<') and result.endswith('>'), result)
+
     def testBasic1(self):
         mock_socket.reply_with(b"220 Hola mundo")
         # connects
diff --git a/Misc/NEWS.d/next/Library/2026-03-05-15-20-18.gh-issue-145552.80p_Cr.rst b/Misc/NEWS.d/next/Library/2026-03-05-15-20-18.gh-issue-145552.80p_Cr.rst
new file mode 100644
index 00000000000000..8c074d08e79380
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-03-05-15-20-18.gh-issue-145552.80p_Cr.rst
@@ -0,0 +1 @@
+Fix ``smtplib.quoteaddr()`` to ensure the returned address always has a closing ``>`` when the input starts with ``<`` but ``email.utils.parseaddr()`` fails to parse it.