diff --git a/requests/exceptions.py b/requests/exceptions.py
index 0e9c820c..c412ec98 100644
--- a/requests/exceptions.py
+++ b/requests/exceptions.py
@@ -25,6 +25,10 @@ class RequestException(IOError):
         super(RequestException, self).__init__(*args, **kwargs)
 
 
+class InvalidJSONError(RequestException):
+    """A JSON error occurred."""
+
+
 class HTTPError(RequestException):
     """An HTTP error occurred."""
 
diff --git a/requests/models.py b/requests/models.py
index 34b672c2..93b901b4 100644
--- a/requests/models.py
+++ b/requests/models.py
@@ -29,7 +29,7 @@ from .auth import HTTPBasicAuth
 from .cookies import cookiejar_from_dict, get_cookie_header, _copy_cookie_jar
 from .exceptions import (
     HTTPError, MissingSchema, InvalidURL, ChunkedEncodingError,
-    ContentDecodingError, ConnectionError, StreamConsumedError)
+    ContentDecodingError, ConnectionError, StreamConsumedError, InvalidJSONError)
 from ._internal_utils import to_native_string, unicode_is_ascii
 from .utils import (
     guess_filename, get_auth_from_url, requote_uri,
@@ -466,7 +466,12 @@ class PreparedRequest(RequestEncodingMixin, RequestHooksMixin):
             # urllib3 requires a bytes-like body. Python 2's json.dumps
             # provides this natively, but Python 3 gives a Unicode string.
             content_type = 'application/json'
-            body = complexjson.dumps(json)
+
+            try:
+              body = complexjson.dumps(json, allow_nan=False)
+            except ValueError as ve:
+              raise InvalidJSONError(ve, request=self)
+
             if not isinstance(body, bytes):
                 body = body.encode('utf-8')
 
diff --git a/tests/test_requests.py b/tests/test_requests.py
index 223c36e3..8f3914ee 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -24,7 +24,7 @@ from requests.cookies import (
 from requests.exceptions import (
     ConnectionError, ConnectTimeout, InvalidSchema, InvalidURL,
     MissingSchema, ReadTimeout, Timeout, RetryError, TooManyRedirects,
-    ProxyError, InvalidHeader, UnrewindableBodyError, SSLError, InvalidProxyURL)
+    ProxyError, InvalidHeader, UnrewindableBodyError, SSLError, InvalidProxyURL, InvalidJSONError)
 from requests.models import PreparedRequest
 from requests.structures import CaseInsensitiveDict
 from requests.sessions import SessionRedirectMixin
@@ -2566,3 +2566,8 @@ class TestPreparingURLs(object):
         r = requests.Request('GET', url=input, params=params)
         p = r.prepare()
         assert p.url == expected
+
+    def test_post_json_nan(self, httpbin):
+        data = {"foo": float("nan")}
+        with pytest.raises(requests.exceptions.InvalidJSONError):
+          r = requests.post(httpbin('post'), json=data)
\ No newline at end of file