diff --git a/django/http/parsers.py b/django/http/parsers.py
index 236cd318ab..d99a2b7d35 100644
--- a/django/http/parsers.py
+++ b/django/http/parsers.py
@@ -70,6 +70,11 @@ class JSONParser(BaseParser):
     def parse(self, request):
         from django.http import HttpRequest
 
+        def strict_constant(o):
+            raise ValueError(
+                "Out of range float values are not JSON compliant: " + repr(o)
+            )
+
         if isinstance(request, HttpRequest):
             request = request.body
-        return json.loads(request), MultiValueDict()
+        return json.loads(request, parse_constant=strict_constant), MultiValueDict()
diff --git a/tests/requests_tests/test_parsers.py b/tests/requests_tests/test_parsers.py
index c9ba5e001a..9769f3b614 100644
--- a/tests/requests_tests/test_parsers.py
+++ b/tests/requests_tests/test_parsers.py
@@ -60,3 +60,13 @@ class TestParsers(SimpleTestCase):
         msg = "You cannot change parsers after processing the request's content."
         with self.assertRaisesMessage(AttributeError, msg):
             request.parsers = []
+
+    def test_json_strict(self):
+        parser = JSONParser()
+
+        msg_base = "Out of range float values are not JSON compliant: '%s'"
+        for value in ["Infinity", "-Infinity", "NaN"]:
+            with self.subTest(value=value):
+                msg = msg_base % value
+                with self.assertRaisesMessage(ValueError, msg):
+                    parser.parse(bytes(value.encode()))