Abstract: The finite difference approximation of two-dimension poisson equation would create a block-tridiagonal equation system．An algorithm which is suitable with the Compute Unified Device Architecture(CUDA)was proposed．Through a discrete sine transform,the computation task could be divided into several completely independent parts,after solving these parts in parallel,the final result could be obtained through another discrete sine transform．Only two global synchronizing is needed during the computation．After carefully optimized,an acceleration rate of more than 10times is obtained.

Key words: Poisson equation,Compute unified device architecture,Parallel computing,Block-tridiagonal equation