diff --git a/rest_framework/parsers.py b/rest_framework/parsers.py
index 5ebaeca2e..7a256276a 100644
--- a/rest_framework/parsers.py
+++ b/rest_framework/parsers.py
@@ -22,6 +22,7 @@ from django.utils.six.moves.urllib import parse as urlparse
 
 from rest_framework import renderers
 from rest_framework.exceptions import ParseError
+from rest_framework.settings import api_settings
 from rest_framework.utils import json
 
 
@@ -53,6 +54,7 @@ class JSONParser(BaseParser):
     """
     media_type = 'application/json'
     renderer_class = renderers.JSONRenderer
+    strict = api_settings.STRICT_JSON
 
     def parse(self, stream, media_type=None, parser_context=None):
         """
@@ -63,7 +65,8 @@ class JSONParser(BaseParser):
 
         try:
             decoded_stream = codecs.getreader(encoding)(stream)
-            return json.load(decoded_stream)
+            parse_constant = json.strict_constant if self.strict else None
+            return json.load(decoded_stream, parse_constant=parse_constant)
         except ValueError as exc:
             raise ParseError('JSON parse error - %s' % six.text_type(exc))
 
diff --git a/rest_framework/renderers.py b/rest_framework/renderers.py
index a87eb1889..90f516b35 100644
--- a/rest_framework/renderers.py
+++ b/rest_framework/renderers.py
@@ -61,6 +61,7 @@ class JSONRenderer(BaseRenderer):
     encoder_class = encoders.JSONEncoder
     ensure_ascii = not api_settings.UNICODE_JSON
     compact = api_settings.COMPACT_JSON
+    strict = api_settings.STRICT_JSON
 
     # We don't set a charset because JSON is a binary encoding,
     # that can be encoded as utf-8, utf-16 or utf-32.
@@ -101,7 +102,7 @@ class JSONRenderer(BaseRenderer):
         ret = json.dumps(
             data, cls=self.encoder_class,
             indent=indent, ensure_ascii=self.ensure_ascii,
-            separators=separators
+            allow_nan=not self.strict, separators=separators
         )
 
         # On python 2.x json.dumps() returns bytestrings if ensure_ascii=True,
diff --git a/rest_framework/settings.py b/rest_framework/settings.py
index 3f3c9110a..bc42c38a6 100644
--- a/rest_framework/settings.py
+++ b/rest_framework/settings.py
@@ -110,6 +110,7 @@ DEFAULTS = {
     # Encoding
     'UNICODE_JSON': True,
     'COMPACT_JSON': True,
+    'STRICT_JSON': True,
     'COERCE_DECIMAL_TO_STRING': True,
     'UPLOADED_FILES_USE_URL': True,
 
diff --git a/tests/test_parsers.py b/tests/test_parsers.py
index 2499bfa3a..0a18aad1a 100644
--- a/tests/test_parsers.py
+++ b/tests/test_parsers.py
@@ -1,7 +1,8 @@
 # -*- coding: utf-8 -*-
-
 from __future__ import unicode_literals
 
+import math
+
 import pytest
 from django import forms
 from django.core.files.uploadhandler import (
@@ -9,7 +10,7 @@ from django.core.files.uploadhandler import (
 )
 from django.http.request import RawPostDataException
 from django.test import TestCase
-from django.utils.six.moves import StringIO
+from django.utils.six import BytesIO, StringIO
 
 from rest_framework.exceptions import ParseError
 from rest_framework.parsers import (
@@ -42,7 +43,6 @@ class TestFileUploadParser(TestCase):
     def setUp(self):
         class MockRequest(object):
             pass
-        from io import BytesIO
         self.stream = BytesIO(
             "Test text file".encode('utf-8')
         )
@@ -129,6 +129,24 @@ class TestFileUploadParser(TestCase):
         self.parser_context['request'].META['HTTP_CONTENT_DISPOSITION'] = disposition
 
 
+class TestJSONParser(TestCase):
+    def bytes(self, value):
+        return BytesIO(value.encode('utf-8'))
+
+    def test_float_strictness(self):
+        parser = JSONParser()
+
+        # Default to strict
+        for value in ['Infinity', '-Infinity', 'NaN']:
+            with pytest.raises(ParseError):
+                parser.parse(self.bytes(value))
+
+        parser.strict = False
+        assert parser.parse(self.bytes('Infinity')) == float('inf')
+        assert parser.parse(self.bytes('-Infinity')) == float('-inf')
+        assert math.isnan(parser.parse(self.bytes('NaN')))
+
+
 class TestPOSTAccessed(TestCase):
     def setUp(self):
         self.factory = APIRequestFactory()
diff --git a/tests/test_renderers.py b/tests/test_renderers.py
index ccc910c63..5f4aa51a3 100644
--- a/tests/test_renderers.py
+++ b/tests/test_renderers.py
@@ -358,6 +358,19 @@ class JSONRendererTests(TestCase):
         with self.assertRaises(TypeError):
             JSONRenderer().render(x)
 
+    def test_float_strictness(self):
+        renderer = JSONRenderer()
+
+        # Default to strict
+        for value in [float('inf'), float('-inf'), float('nan')]:
+            with pytest.raises(ValueError):
+                renderer.render(value)
+
+        renderer.strict = False
+        assert renderer.render(float('inf')) == b'Infinity'
+        assert renderer.render(float('-inf')) == b'-Infinity'
+        assert renderer.render(float('nan')) == b'NaN'
+
     def test_without_content_type_args(self):
         """
         Test basic JSON rendering.
diff --git a/tests/test_utils.py b/tests/test_utils.py
index 9619776d6..c5e6f26dc 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -198,3 +198,10 @@ class JsonFloatTests(TestCase):
 
         with self.assertRaises(ValueError):
             json.loads("NaN")
+
+
+@override_settings(STRICT_JSON=False)
+class NonStrictJsonFloatTests(JsonFloatTests):
+    """
+    'STRICT_JSON = False' should not somehow affect internal json behavior
+    """