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?
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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:
the arrow symbol. Was that based on a dingbat font symbol? If so, should be easy to recreate.
the right hand angled outline. Copy a rectangular area from just left of the arrow symbol over the scaled-up right hand end, then use the polygon select tool to delete from this leaving a crisp edge. Angles look to be 45deg which will male it easier.
possibly the dividing line between the two types of fill. Copying and pasting will fix this.