diff --git a/Misc/NEWS.d/next/Library/2020-03-11-07-44-06.bpo-31122.zIQ80l.rst b/Misc/NEWS.d/next/Library/2020-03-11-07-44-06.bpo-31122.zIQ80l.rst
new file mode 100644
index 00000000000000..2e70f7aee65c83
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-03-11-07-44-06.bpo-31122.zIQ80l.rst
@@ -0,0 +1 @@
+ssl.wrap_socket() now raises ssl.SSLEOFError rather than OSError when peer closes connection during TLS negotiation
\ No newline at end of file
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index a8c339d9f33344..28796b376e8623 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -805,10 +805,11 @@ PySSL_SetError(PySSLSocket *sslsock, int ret, const char *filename, int lineno)
                         errno = err.c;
                         return PyErr_SetFromErrno(PyExc_OSError);
                     }
-                    Py_INCREF(s);
-                    s->errorhandler();
-                    Py_DECREF(s);
-                    return NULL;
+                    else {
+                        p = PY_SSL_ERROR_EOF;
+                        type = PySSLEOFErrorObject;
+                        errstr = "EOF occurred in violation of protocol";
+                    }
                 } else { /* possible? */
                     p = PY_SSL_ERROR_SYSCALL;
                     type = PySSLSyscallErrorObject;