In this paper, an axial field switched-flux permanent magnet (AFSFPM) machine with stator-PM, which has a high power/torque density and efficiency feature as well as shorter axial length, is designed, analyzed and controlled. The topology, operating principle and design procedure of the AFSFPM machine are labored and discussed. The electromagnetic performance, including the flux linkage, back-EMF, cogging torque, winding inductance and field-control capability, are studied based on 3-D finite-element analysis (FEA). In order to investigate the operating performance of the machine in the whole speed range, a continuous-control-set model predictive control (MPC) method for the AFSFPM machine is proposed. Based on the stage control targets, the maximum torque per ampere (MTPA) and maximum output power flux-weakening strategies are presented in constant torque and constant power regions, respectively. Finally, a prototype of AFSFPM machine has been manufactured and experimentally evaluated and the results show that the MTPA strategy increases the load capability and the flux-weakening strategy broadens the constant power operation range. Moreover, the anti-load-disturbance capacity and dynamic response performance are improved under the MPC method. As a result, the proposed AFSFPM machine drive system is excellent alternative for electrical vehicles (EVs) or hybrid EVs (HEVs).