diff --git a/pkgs/racket-pkgs/racket-test/tests/json/json.rkt b/pkgs/racket-pkgs/racket-test/tests/json/json.rkt
index f38ec511ae..28fc492673 100644
--- a/pkgs/racket-pkgs/racket-test/tests/json/json.rkt
+++ b/pkgs/racket-pkgs/racket-test/tests/json/json.rkt
@@ -35,6 +35,9 @@
         (not (jsexpr? '#hasheq([1 . 1])))
         (not (jsexpr? '#hasheq(["x" . 1])))
         (not (jsexpr? '#hasheq(['() . 1])))
+        (not (jsexpr? (/ 1.0 0.0)))
+        (not (jsexpr? (/ -1.0 0.0)))
+        (not (jsexpr? (/ 0.0 0.0)))
         )
   ;; other `null' values
   (parameterize ([json-null #\null])
diff --git a/racket/collects/json/main.rkt b/racket/collects/json/main.rkt
index b1b21edfe6..7c3544faa1 100644
--- a/racket/collects/json/main.rkt
+++ b/racket/collects/json/main.rkt
@@ -18,7 +18,7 @@
 (define (jsexpr? x #:null [jsnull (json-null)])
   (let loop ([x x])
     (or (exact-integer? x)
-        (inexact-real? x)
+        (real-real? x)
         (boolean? x)
         (string? x)
         (eq? x jsnull)
@@ -26,6 +26,9 @@
         (and (hash? x) (for/and ([(k v) (in-hash x)])
                          (and (symbol? k) (loop v)))))))
 
+(define (real-real? x) ; not nan or inf
+  (and (inexact-real? x) (not (member x '(+nan.0 +inf.0 -inf.0)))))
+
 ;; ----------------------------------------------------------------------------
 ;; Generation: Racket -> JSON
 
@@ -64,7 +67,7 @@
     (write-string (regexp-replace* rx-to-encode str escape) o)
     (write-bytes #"\"" o))
   (let loop ([x x])
-    (cond [(or (exact-integer? x) (inexact-real? x)) (write x o)]
+    (cond [(or (exact-integer? x) (real-real? x)) (write x o)]
           [(eq? x #f)     (write-bytes #"false" o)]
           [(eq? x #t)     (write-bytes #"true" o)]
           [(eq? x jsnull) (write-bytes #"null" o)]