I have tried burning avi to dvd but it take more than 3 hours to convert avi to dvd format. Is there any other way can speed it up? Will it be faster if I convert avi to MPEG2 or DVD before I burn the movie to DVD disk?
Yes the burning will be faster.
But the time needed to recode the movie will stay the same (assuming you use the same codec). I never did it that way round - I always convert MPEG2 -> AVI/Xvid, but that needs hours as well, I think much longer than AVI(Xvid,Divx) -> MPEG2 (maybe factor 3 or 3? not sure).
Maybe you can find more efficient recoding software than you use now. Look at www.doom9.net, they have lots of info about digital video, audio, recoding etc.