diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 250f443..e4876fd 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -319,6 +319,11 @@
         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))
 
     def test_referenceImplementation(self):
         # Compare the python implementation with results from the original
diff --git a/Misc/NEWS b/Misc/NEWS
index 95d6e11..9027ec8 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -34,6 +34,8 @@
 Library
 -------
 
+- Issue #24620: Random.setstate() now validates the value of state last element.
+
 - Issue #13938: 2to3 converts StringTypes to a tuple. Patch from Mark Hammond.
 
 - Issue #24611: Fixed compiling the posix module on non-Windows platforms
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index 8bb9e37..480df92 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -363,6 +363,10 @@
     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);