A model of a stand-alone Proton Exchange Membrane Fuel Cell PEMFC power supply for AC motor application is studied in this paper. As an AC load, a permanent magnet synchronous motor PMSM is chosen. The power conversion chain is basically composed of DC-DC boost converter and DC-AC inverter to increase and regulate the generated voltage by the PEMFC in order to satisfy the load requirements. Then, a mathematical model of each component is presented. In order to control the PEMFC power system, SMC and vector control are applied. Moreover, the PEMFC characteristics, the proposed controls and the PMSM responses are discussed. Simulations are performed using MATLAB/Simulink software.