Based on the differential scheme,presents a numerical method of pricing for American put options.Firstly,the partial differential equation satisfied by the option price is transformed into a series of differential equations.Then,these differential equations are solved by the iterative method.The numerical method includes the implicit finite difference method and the explicit finite difference method and these two methods are compared.Finally,a numerical example is given and the validity of the algorithm is checked by a series of experiments.Some useful results are obtained for its application in the option markets.