Range Extender Electric Vehicle (REEV) is an interesting and promising concept in automotive field due to it provides a simple and effective way to solve the problem of limited driving distance in EVs. Firstly, an ICE/PM/TTRB APU is developed in this paper, in which the three-phase thyristor rectification bridge is utilized, thus it is more economic and easier to control than the traditional ICE/PM/ISG APU. Then, the speed switching-power following APU cooperative control strategy is presented, in which the engine speed and APU power control system are designed independently. Through adjusting the engine speed and the output power of the TTRB, the proposed control strategy forces the engine runs along the optimal Brake Specific Fuel Consumption (BSFC) curve. Finally, the joint simulation model based on AVL Cruise and Matlab/Simulink is developed. The simulation results show that the proposed APU control strategy is excellent in aspects of power following and speed controlling accuracy, SOC fluctuation range and operating points distribution. The experimental tests based on a prototype vehicle are also presented in which the effectiveness of the proposed APU structure and the associated control strategy are validated experimentally.