diff --git a/Lib/test/test_csv.py b/Lib/test/test_csv.py
index 8ca1e62..55796a2 100644
--- a/Lib/test/test_csv.py
+++ b/Lib/test/test_csv.py
@@ -225,6 +225,15 @@
         self.assertRaises(csv.Error, self._read_test, ['a,b\nc,d'], [])
         self.assertRaises(csv.Error, self._read_test, ['a,b\r\nc,d'], [])
 
+    def test_read_eof(self):
+        self._read_test(['a,"'], [['a', '']])
+        self._read_test(['"a'], [['a']])
+        self._read_test(['^'], [['\n']], escapechar='^')
+        self.assertRaises(csv.Error, self._read_test, ['a,"'], [], strict=True)
+        self.assertRaises(csv.Error, self._read_test, ['"a'], [], strict=True)
+        self.assertRaises(csv.Error, self._read_test,
+                          ['^'], [], escapechar='^', strict=True)
+
     def test_read_escape(self):
         self._read_test(['a,\\b,c'], [['a', 'b', 'c']], escapechar='\\')
         self._read_test(['a,b\\,c'], [['a', 'b,c']], escapechar='\\')
diff --git a/Misc/NEWS b/Misc/NEWS
index a67f7c5..f705688 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -31,6 +31,9 @@
 Library
 -------
 
+- Issue #16013: Fix CSV Reader parsing issue with ending quote characters.
+  Patch by Serhiy Storchaka.
+
 - Issue #15421: Fix an OverflowError in Calendar.itermonthdates() after
   datetime.MAXYEAR.  Patch by Cédric Krier.
 
diff --git a/Modules/_csv.c b/Modules/_csv.c
index 8380990..cc87bad 100644
--- a/Modules/_csv.c
+++ b/Modules/_csv.c
@@ -788,9 +788,14 @@
         lineobj = PyIter_Next(self->input_iter);
         if (lineobj == NULL) {
             /* End of input OR exception */
-            if (!PyErr_Occurred() && self->field_len != 0)
-                PyErr_Format(_csvstate_global->error_obj,
-                             "newline inside string");
+            if (!PyErr_Occurred() && (self->field_len != 0 ||
+                                      self->state == IN_QUOTED_FIELD)) {
+                if (self->dialect->strict)
+                    PyErr_SetString(_csvstate_global->error_obj,
+                                    "unexpected end of data");
+                else if (parse_save_field(self) >= 0)
+                    break;
+            }
             return NULL;
         }
         if (!PyUnicode_Check(lineobj)) {