Both forms are correct.

Both spellings of favourite/favorite exist in English, however, favourite a is British English word while favorite is American English. What is interesting both words have the same, two ways of pronunciation – fay-vuh-rit or fay-vrit– both correct and can be used in British and American spelling. The problem of -or and -our ending of words is common and today we use the former in British and the latter in American. This rule is known to be introduced by American lexicographer Noah Webster, who is said to be the father of American spellings of words.

Correct spelling, this spelling is from American English.

Correct spelling, this spelling is used in British English.

Definition of favourite/favorite:
1. noun, a thing or a person that one prefers to another; also a person who is considered the most probable to win in a competition
Johnny loves his toys, but this teddy is his favourite.
I don’t think we have any favourite in this contest so far.
2. adjective, most liked, preferred
My favorite ice cream is chocolate chip.