In this paper，a fast algorithm is developed to compute two-dimensional Discrete Fourier Transform (DFT) of an array of NxM complex number points using FPT，where M=2^m,N=2^m-r+1,1≤r≤m.As compared with the conventional radix-2 two-dimensional Fast Fourier Transforms,this new algorithm requires less number of multiplications (decrease by 30-40%) and same number of additions, so that elevates the computing accuracy. The number of multiplications and additions are respectively M_u=1/2NMlog₂M-3/2NM+N²+N(1+log₂M-log₂N) A_d= NMlog₂MN. This algorithm also has the advantage to adopt the parallel algorithm.