Celui usually means “this one”, “that one”, or “the one”.

Celui que j’aime, c’est le bleu. The blue one is the one I like.

It is often suffixed with -ci to specify “this” or -là to specify “that”.

• Quel jouet veux-tu ? Which toy do you want?
  
  – Celui-ci … le crocodile. This one… the crocodile.
  
  – Pas celui-là, le joli ours ? Not that one, the nice bear?
  
  – Pas du tout, maman ! No way, mom!

The way you worded it would mean something like “the one of mine”, which is equally impossible in English and French. If you mean “mine”, the one you want is le mien.