diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index e64804556db..4b5232fe21d 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -338,6 +338,11 @@ class MersenneTwister_TestBasicOps(TestBasicOps, unittest.TestCase):
         self.assertRaises(TypeError, self.gen.setstate, (2, ('a',)*625, None))
         # Last element s/b an int also
         self.assertRaises(TypeError, self.gen.setstate, (2, (0,)*624+('a',), None))
+        # Last element s/b between 0 and 624
+        with self.assertRaises((ValueError, OverflowError)):
+            self.gen.setstate((2, (1,)*624+(625,), None))
+        with self.assertRaises((ValueError, OverflowError)):
+            self.gen.setstate((2, (1,)*624+(-1,), None))
 
         # Little trick to make "tuple(x % (2**32) for x in internalstate)"
         # raise ValueError. I cannot think of a simple way to achieve this, so
diff --git a/Misc/NEWS b/Misc/NEWS
index d38c4146f5a..1a67632e918 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -66,6 +66,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #24620: Random.setstate() now validates the value of state last element.
+
 - Issue #22153: Improve unittest docs. Patch from Martin Panter and evilzero.
 
 - Issue #24206: Fixed __eq__ and __ne__ methods of inspect classes.
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index 4377ee0cf4d..416e266f0bd 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -340,6 +340,10 @@ random_setstate(RandomObject *self, PyObject *state)
     index = PyLong_AsLong(PyTuple_GET_ITEM(state, i));
     if (index == -1 && PyErr_Occurred())
         return NULL;
+    if (index < 0 || index > N) {
+        PyErr_SetString(PyExc_ValueError, "invalid state");
+        return NULL;
+    }
     self->index = (int)index;
 
     Py_INCREF(Py_None);