I want to express my appreciation to someone who helped me, Can I say: I feel grateful to this person for his help on the project? (I don't want to use thank)
Your usage of 'grateful' is grammatically correct - an acceptable usage is
grateful (to somebody) (for something)
For example - I am extremely grateful to all the teachers for their help.
Personally I would say "I am grateful to...." - for me it seems more natural, but that really comes down to personal choice.