I have image which as black background and i want to remove the black background and use the image as transparent only color smoke.
You don't necessarily use the Mix Shader with the alpha channel of the image. You can also use the color channel. So on the darker areas the first shader (Transparent) will dominate and on the lighter parts the second shader (Diffuse) will get a higher value. You can plug a ColorRamp before the Fac shocket to finetune the silhouette. Of course you can use images with white background, just swap the transparent and diffuse shaders.
For anyone that comes back, here's a simpler node setup. Just run the image texture's color output through a principled shader's alpha attribute. That's the quick and dirty way, but an added color ramp in between gets a much nicer result. With a bit of tweaking, this should allow you to make most images transparent.