I would like to double the size of this image without causing any pixelization.
Can you please let me know how can it be done?
It's going to largely depend on the original size. Photoshop is many things, but it's not magic. It can do some fairly impressive things with pixel interpolation but there's a limit.
I would suggest using "Image" -> "Image Size..." and scaling it that way - at least it will scale consistently. I am not quite sure how exact you need to be when you say "any" pixelation; this method may allow you to scale this with a minimum (i.e., not noticeable by anyone who's not looking for it) amount.
If you're really worried about this I'd create it in a vector-based program like Illustrator (it looks like it'd be a fairly simple job) so you can scale it to any size your heart desires.
With this particular image, I'd scale it up with Image Size at 200%, using bicubic interpolation, and then correct the issues.
The only areas where pixelation will be noticeable will be: