Abstract: Recursion is a more powerful algorithm than iterative loop. On the one hand, for every iterative loop there is always an equivalent recursion. On the other hand, some problems, insoluble by means of iterative loop, are often solved by recursion. The Lattice Point Problem is typical one of these problems.By constructing an effective algorithm for the Lattice Point Problem, we have firstly discussed how to choose a proper algorithm depending on the inherent structural relations of a certain problem.