Are there any easy way to make the white background transparent?
HOW to make a transparent background for this or any image depends on how you intend to use the "cut-out" version. If you simply want to remove the background, the least-destructive and adjustable way is to use a mask.
Assuming you want to keep the "white" color in the subject of the image, most normal removal methods, like using "multiply" or the magic wand, will remove most of the white inside and outside of your character. Using a mask, you just "paint" the area you want to hide. In the case of your image, this is relatively simple and doesn't take much time while still being adjusted to your preference. Here is a quick PNG with the background masked:
Now, if you mean to overlay this character onto another background, what I normally do is use a combination of a mask and a "multiply" blending mode in order to make the edge softer and hide any white "halo" around the subject. To do this, I would take the same mask I drew for the character, move that to a white background layer and then change the subject layer blending mode to "multiply". I would then just "cut-in" the mask as necessary to blend the outline of the subject more with whatever background these two layers are on top of.