The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.