They're both correct. "Centre" is the UK spelling (following the French fashion, silent 'e' and so on), and "center" is the US spelling (a revision by Noah Webster, I think, to make the word closer to its original spelling in Greek, as well as more phonetic). The spelling you choose depends on the spellings of other words: "my favourite colour is in the centre"(UK) and "my favorite color is in the center"(US) are both correct, but "my favourite colour is in the center" looks wrong from both sides of the pond. The trick is to stay consistent.

I think your question is " What is the difference between center and centre? " and the answer, these two word are the same, it's just that one is American English while another is British English.