diff --git a/src/write.jl b/src/write.jl
index bfff8a1..37d9803 100644
--- a/src/write.jl
+++ b/src/write.jl
@@ -284,17 +284,32 @@ end
     if isinf(x)
         # Although this is non-standard JSON, "Infinity" is commonly used.
         # See https://docs.python.org/3/library/json.html#infinite-and-nan-number-values.
-        if sign(x) == -1
-            @writechar '-'
+        return if sign(x) == 1
+            write(RawType(), buf, pos, len, Val(Inf))
+        else
+            write(RawType(), buf, pos, len, Val(-Inf))
         end
-        @writechar 'I' 'n' 'f' 'i' 'n' 'i' 't' 'y'
-        return buf, pos, len
+    end
+    if isnan(x)
+        return write(RawType(), buf, pos, len, Val(NaN))
     end
     @check Ryu.neededdigits(T)
     pos = Ryu.writeshortest(buf, pos, x)
     return buf, pos, len
 end
 
+function rawbytes(::Val{T}) where T
+    codeunits(
+        if T === Inf
+            "Infinity"
+        elseif T === -Inf
+            "-Infinity"
+        else
+            "NaN"
+        end
+    )
+end
+
 const NEEDESCAPE = Set(map(UInt8, ('"', '\\', '\b', '\f', '\n', '\r', '\t')))
 
 function escapechar(b)
diff --git a/test/json.jl b/test/json.jl
index 98b1e2c..c42c56c 100644
--- a/test/json.jl
+++ b/test/json.jl
@@ -46,6 +46,19 @@ end
     @test JSON3.read("Inf"; allow_inf=true) === Inf
     @test JSON3.read("Infinity"; allow_inf=true) === Inf
     @test JSON3.read("-Infinity"; allow_inf=true) === -Inf
+
+    JSON3.rawbytes(::Val{Inf}) = codeunits("1e1000")
+    JSON3.rawbytes(::Val{-Inf}) = codeunits("__-inf__")
+    JSON3.rawbytes(::Val{NaN}) = codeunits("__nan__")
+
+    @test JSON3.write([Inf], allow_inf=true) == "[1e1000]"
+    @test JSON3.write([-Inf], allow_inf=true) == "[__-inf__]"
+    @test JSON3.write([NaN], allow_inf=true) == "[__nan__]"
+
+    # delete the methods to avoid affecting other tests
+    Base.delete_method.(methods(JSON3.rawbytes, (Val{Inf},)))
+    Base.delete_method.(methods(JSON3.rawbytes, (Val{-Inf},)))
+    Base.delete_method.(methods(JSON3.rawbytes, (Val{NaN},)))
 end
 
 @testset "Char" begin