Range extender hybrid vehicles have the advantages of better dynamics and longer driving range while reducing pollution and fuel consumption. This work focuses on the control strategy of an Auxiliary Power Unit (APU) operating in power generation mode for a range-extender mixer truck. When an operating point is switched, the engine speed and generator torque of the APU will switch accordingly. In order to ensure APU fast and stable adjustment to meet the power demand of the vehicle as well as operate at the lowest fuel consumption, a fuzzy adaptive PID coordination control strategy based on particle swarm optimization (PSO) is proposed to control the APU. The optimal operating curve of APU is calculated by coupling the engine and generator first. Then, the adaptive PID algorithm is used to control the speed and torque of the APU in a dual closed loop. The PSO is used to optimize the PID control parameter. Through hardware-in-the-loop tests under different working conditions, the control strategy is verified to be effective and real-time. The results show that the proposed control strategy can coordinate the operating of engine and generator and control the APU to track target power stably and quickly under minimum fuel consumption. Compared with traditional PID control strategy, the overshoot, regulation time and steady-state error are reduced by 55.1%, 11.1% and 77.3%, respectively.