I feel my manager wants to promote him instead of me in next 6 months
(mostly because he is in the team longer than me). Although my
performance in the project is better than him.
In this situation, what can I bring up this to my manager?
If you feel you deserve a promotion, you should ask for one. Find a quiet time to talk and start with something like "Boss, I think I deserve a promotion." Then go into the reasons why you deserve one.
Talk about how hard you have worked. Mention the difference you have made to the company. Talk about how long it has been since you joined (or since you were last promoted). Talk about the kinds of things you want to do going forward. Explain why this will be very valuable to the company. Make sure you indicate what position you want to get promoted into.
Whatever you do, do not indicate that you want a promotion simply because you believe your coworker will be getting a promotion 6 months down the road. Do not indicate that you believe your performance on your current project has been better than this coworker. Whatever is going on with your coworker is simply not relevant to you or your potential promotion. Talking about someone else is a very weak argument.