Electric power steering system (EPS) with traditional power supply can't provide enough power for heavy-duty vehicle to turn at low speed. To solve the problem, a novel EPS with hybrid power supply was constructed. In this paper, firstly, mathematical model of the EPS with hybrid power supply was established including model of hybrid power supply system and basic model of EPS. Then the power mode recognition was obtained according to the certain threshold of steering resistance torque, state of charge (SOC) of super-capacitor and output voltage of the vehicle power supply, and the corresponding finite automaton model was built. The EPS system with hybrid power supply was regarded as a hybrid system due to continuous event in a single mode and discrete event during mode switching process, thus the multi-mode switching control strategy was proposed. Taken the different characteristics of hybrid power supply in different power modes into account, the corresponding local controllers were designed which were consisted of fuzzy-PID controller, active disturbance rejection controller (ADRC) and sliding mode controller. Besides, the fuzzy supervisory controller was also designed to ensure the stability of the hybrid system during mode switching process. The simulation results show that the local controllers can achieve fast and accurate track of target current in each power mode, and the fuzzy supervisor can effectively ensure the stability of the switching process, which demonstrates the feasibility of the control strategy.