diff --git a/src/eval.c b/src/eval.c
index 1471568..cf908d1 100644
--- a/src/eval.c
+++ b/src/eval.c
@@ -628,6 +628,9 @@
 static void f_invert(typval_T *argvars, typval_T *rettv);
 static void f_isdirectory(typval_T *argvars, typval_T *rettv);
 static void f_islocked(typval_T *argvars, typval_T *rettv);
+#if defined(FEAT_FLOAT) && defined(HAVE_MATH_H)
+static void f_isnan(typval_T *argvars, typval_T *rettv);
+#endif
 static void f_items(typval_T *argvars, typval_T *rettv);
 #ifdef FEAT_JOB
 # ifdef FEAT_CHANNEL
@@ -8320,6 +8323,9 @@
     {"invert",		1, 1, f_invert},
     {"isdirectory",	1, 1, f_isdirectory},
     {"islocked",	1, 1, f_islocked},
+#if defined(FEAT_FLOAT) && defined(HAVE_MATH_H)
+    {"isnan",		1, 1, f_isnan},
+#endif
     {"items",		1, 1, f_items},
 #ifdef FEAT_JOB
 # ifdef FEAT_CHANNEL
@@ -14740,6 +14746,18 @@
     clear_lval(&lv);
 }
 
+#if defined(FEAT_FLOAT) && defined(HAVE_MATH_H)
+/*
+ * "isnan()" function
+ */
+    static void
+f_isnan(typval_T *argvars, typval_T *rettv)
+{
+    rettv->vval.v_number = argvars[0].v_type == VAR_FLOAT
+					    && isnan(argvars[0].vval.v_float);
+}
+#endif
+
 static void dict_list(typval_T *argvars, typval_T *rettv, int what);
 
 /*
diff --git a/src/json.c b/src/json.c
index 7b85cd2..6eadd2e 100644
--- a/src/json.c
+++ b/src/json.c
@@ -16,6 +16,12 @@
 #include "vim.h"
 
 #if defined(FEAT_EVAL) || defined(PROTO)
+
+#if defined(FEAT_FLOAT) && defined(HAVE_MATH_H)
+  /* for isnan() and isinf() */
+# include <math.h>
+#endif
+
 static int json_encode_item(garray_T *gap, typval_T *val, int copyID, int options);
 static int json_decode_item(js_read_T *reader, typval_T *res, int options);
 
@@ -267,8 +273,20 @@
 
 	case VAR_FLOAT:
 #ifdef FEAT_FLOAT
-	    vim_snprintf((char *)numbuf, NUMBUFLEN, "%g", val->vval.v_float);
-	    ga_concat(gap, numbuf);
+# if defined(HAVE_MATH_H)
+	    if ((options & JSON_JS) && isnan(val->vval.v_float))
+		ga_concat(gap, (char_u *)"NaN");
+	    else if ((options & JSON_JS) && isinf(val->vval.v_float))
+		ga_concat(gap, (char_u *)"Infinity");
+	    else if (isnan(val->vval.v_float) || isinf(val->vval.v_float))
+		ga_concat(gap, (char_u *)"null");
+	    else
+# endif
+	    {
+		vim_snprintf((char *)numbuf, NUMBUFLEN, "%g",
+							   val->vval.v_float);
+		ga_concat(gap, numbuf);
+	    }
 	    break;
 #endif
 	case VAR_UNKNOWN:
@@ -720,9 +738,36 @@
 		}
 		return OK;
 	    }
+#ifdef FEAT_FLOAT
+	    if (STRNICMP((char *)p, "NaN", 3) == 0)
+	    {
+		reader->js_used += 3;
+		if (res != NULL)
+		{
+		    res->v_type = VAR_FLOAT;
+		    res->vval.v_float = 0.0 / 0.0;
+		}
+		return OK;
+	    }
+	    if (STRNICMP((char *)p, "Infinity", 8) == 0)
+	    {
+		reader->js_used += 8;
+		if (res != NULL)
+		{
+		    res->v_type = VAR_FLOAT;
+		    res->vval.v_float = 1.0 / 0.0;
+		}
+		return OK;
+	    }
+#endif
 	    /* check for truncated name */
 	    len = (int)(reader->js_end - (reader->js_buf + reader->js_used));
-	    if ((len < 5 && STRNICMP((char *)p, "false", len) == 0)
+	    if (
+		    (len < 5 && STRNICMP((char *)p, "false", len) == 0)
+#ifdef FEAT_FLOAT
+		    || (len < 8 && STRNICMP((char *)p, "Infinity", len) == 0)
+		    || (len < 3 && STRNICMP((char *)p, "NaN", len) == 0)
+#endif
 		    || (len < 4 && (STRNICMP((char *)p, "true", len) == 0
 			       ||  STRNICMP((char *)p, "null", len) == 0)))
 		return MAYBE;
diff --git a/src/testdir/test_json.vim b/src/testdir/test_json.vim
index 3ac936f..bde7321 100644
--- a/src/testdir/test_json.vim
+++ b/src/testdir/test_json.vim
@@ -16,8 +16,16 @@
 let s:varmb = "s¢cĴgё"
 let s:jsonnr = '1234'
 let s:varnr = 1234
-let s:jsonfl = '12.34'
-let s:varfl = 12.34
+if has('float')
+  let s:jsonfl = '12.34'
+  let s:varfl = 12.34
+  let s:jsoninf = 'null'
+  let s:jsinf = 'Infinity'
+  let s:varinf = 1.0 / 0.0
+  let s:jsonnan = 'null'
+  let s:jsnan = 'NaN'
+  let s:varnan = 0.0 / 0.0
+endif
 
 let s:jsonl1 = '[1,"a",3]'
 let s:varl1 = [1, "a", 3]
@@ -68,6 +76,8 @@
   call assert_equal(s:jsonnr, json_encode(s:varnr))
   if has('float')
     call assert_equal(s:jsonfl, json_encode(s:varfl))
+    call assert_equal(s:jsoninf, json_encode(s:varinf))
+    call assert_equal(s:jsonnan, json_encode(s:varnan))
   endif
 
   call assert_equal(s:jsonl1, json_encode(s:varl1))
@@ -165,6 +175,8 @@
   call assert_equal(s:jsonnr, js_encode(s:varnr))
   if has('float')
     call assert_equal(s:jsonfl, js_encode(s:varfl))
+    call assert_equal(s:jsinf, js_encode(s:varinf))
+    call assert_equal(s:jsnan, js_encode(s:varnan))
   endif
 
   call assert_equal(s:jsonl1, js_encode(s:varl1))
@@ -201,6 +213,8 @@
   call assert_equal(s:varnr, js_decode(s:jsonnr))
   if has('float')
     call assert_equal(s:varfl, js_decode(s:jsonfl))
+    call assert_equal(s:varinf, js_decode(s:jsinf))
+    call assert_true(isnan(js_decode(s:jsnan)))
   endif
 
   call assert_equal(s:varl1, js_decode(s:jsonl1))
diff --git a/src/version.c b/src/version.c
index a04a948..8d858d1 100644
--- a/src/version.c
+++ b/src/version.c
@@ -749,6 +749,8 @@
 static int included_patches[] =
 {   /* Add new patch number below this line */
 /**/
+    1407,
+/**/
     1406,
 /**/
     1405,