He didn't tell her...,

[Silverobama]

He didn't tell her girlfriend the exact time of his arriving home because he wanted to give her girlfriend a surprise.

I wrote the above sentence and I want to make sure if "give somebody a surprise" is natural. Is my sentence natural? If so, how can I use the phrase "give somebody a surprise".

 

[emsr2d2]

He didn't tell her his girlfriend the exact time of his arriving home because he wanted to give her his girlfriend a surprise.

You've mixed up "his" and "her" (at least if I correctly assumed you were talking about the girlfriend of whoever "he" is).
Also, "the exact time of his arriving home", while correct, sounds stilted and old-fashioned. We'd say something like "the exact time he'd be [arriving] home".

I wrote the above sentence and I want to make sure if "give somebody a surprise" is natural. Is my sentence natural? If so, how can I use the phrase "give somebody a surprise".

The way you've used it is OK although most native speakers would probably end that sentence with "... he wanted to surprise her". If you do want to stick with "give someone a surprise", don't repeat "his girlfriend", say "... he wanted to give her a surprise".

Here's what I would write:

He didn't tell his girlfriend exactly what time he'd be home because he wanted to surprise her.