Abstract: A fast algorithm is proposed for the direct discrete summation of Stokes ’ and Hotine ’ s integral,the integral kernels are expressed as the functions of the latitudes of computation point and running point and the longitude-difference between them,the symmetries of the kernels are exploited so that they may only be evaluated once for all the computation points on the same latitude,the computation times of fast algorithm are far less than that of ordinary algorithm.The numerical simulation based on EGM2008 Earth gravitational model shows that the fast algorithm is far more efficient than the oridinary algorithm that the problem of numerical inefficiency can be effectively solved.Besides,the new algorithm retains the attributes of surface integral and can be used to replace 1DFFT for evaluating Stokes ’ or Hotine ’ s integral.