This report analyzes the differences of maximum power point tracking (MPPT) methods by using MATLAB simulations. Considering the small wind power system composed of a small wind turbine, permanent-magnet synchronous generator, three-phase full bridge rectifier, DC/DC converter, MPPT power controller, and load, we will find the problems for using traditional MPPT methods. Here the fuzzy logic control method as well as perturbation and observation method is utilized for the MPPT control under several cases with step, fixed, and variable speed wind. By the MATLAB simulation tests, the fuzzy logic control MPPT method is better than the perturbation and observation method.