diff -uNrp a/Lib/email/_parseaddr.py b/Lib/email/_parseaddr.py
--- a/Lib/email/_parseaddr.py	2019-12-21 16:01:21.340000000 +0800
+++ b/Lib/email/_parseaddr.py	2019-12-21 16:03:22.108000000 +0800
@@ -336,7 +336,12 @@ class AddrlistClass:
         aslist.append('@')
         self.pos += 1
         self.gotonext()
-        return EMPTYSTRING.join(aslist) + self.getdomain()
+        domain = self.getdomain()
+        if not domain:
+            # Invalid domain, return an empty address instead of returning a
+            # local part to denote failed parsing.
+            return EMPTYSTRING
+        return EMPTYSTRING.join(aslist) + domain
 
     def getdomain(self):
         """Get the complete domain name from an address."""
@@ -351,6 +356,10 @@ class AddrlistClass:
             elif self.field[self.pos] == '.':
                 self.pos += 1
                 sdlist.append('.')
+            elif self.field[self.pos] == '@':
+                # bpo-34155: Don't parse domains with two `@` like
+                # `[email protected]@important.com`.
+                return EMPTYSTRING
             elif self.field[self.pos] in self.atomends:
                 break
             else:
diff -uNrp a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
--- a/Lib/email/test/test_email.py	2019-12-21 16:01:21.344000000 +0800
+++ b/Lib/email/test/test_email.py	2019-12-21 16:04:40.564000000 +0800
@@ -2306,6 +2306,20 @@ class TestMiscellaneous(TestEmailBase):
         self.assertEqual(Utils.parseaddr('<>'), ('', ''))
         self.assertEqual(Utils.formataddr(Utils.parseaddr('<>')), '')
 
+    def test_parseaddr_multiple_domains(self):
+        self.assertEqual(
+            Utils.parseaddr('a@b@c'),
+            ('', '')
+        )
+        self.assertEqual(
+            Utils.parseaddr('[email protected]@c'),
+            ('', '')
+        )
+        self.assertEqual(
+            Utils.parseaddr('[email protected]@c'),
+            ('', '')
+        )
+
     def test_noquote_dump(self):
         self.assertEqual(
             Utils.formataddr(('A Silly Person', '[email protected]')),
diff -uNrp a/Misc/NEWS.d/next/Security/2019-05-04-13-33-37.bpo-34155.MJll68.rst b/Misc/NEWS.d/next/Security/2019-05-04-13-33-37.bpo-34155.MJll68.rst
--- a/Misc/NEWS.d/next/Security/2019-05-04-13-33-37.bpo-34155.MJll68.rst	1970-01-01 08:00:00.000000000 +0800
+++ b/Misc/NEWS.d/next/Security/2019-05-04-13-33-37.bpo-34155.MJll68.rst	2019-12-21 16:05:05.292000000 +0800
@@ -0,0 +1 @@
+Fix parsing of invalid email addresses with more than one ``@`` (e.g. a@[email protected].) to not return the part before 2nd ``@`` as valid email address. Patch by maxking & jpic.