With the idea of finite approximation, we study a new solution method for the satellite altimetry problem. Our result shows that if the continental part of the earth is sphere cap, then the solution of satellite altimetry problem can be transformed into a linear system of equations with variants of the coefficients of spherical harmonic series. We prove that the linear system of equations is separated about the orders of spherical harmonic series. By making use of the imitation computation for the EGM96 model, it is concluded that the solution method given in the paper can reach accuracy of 10^(-11). In addition, we also prove that solutions for the Stokes problem, Dirichlet problem and Neumann problem are all particular cases of the satellite altimetry.