Due to its advantages of high positioning accuracy, small torque ripple and high torque density, five-phase hybrid stepping motor has been widely used. In order to further reduce its operation noise and improve the overall efficiency of the system, this paper proposes a space vector pulse width modulation (SVPWM) optimal control strategy of five-phase hybrid stepping motor which can suppress the third harmonic wave. In this paper, the decoupling control model of five-phase hybrid stepping motor considering mutual inductance is established. On this basis, SVPWM control strategy combining two adjacent large vectors and two medium vectors into a mixed voltage vector is adopted, and the corresponding dual-closed-loop control system of five-phase hybrid stepping motor is given. The mixed SVPWM algorithm proposed in this paper can effectively reduce the phase current ripple and harmonic content by using the large and medium vectors in the fundamental wave and the third harmonic coordinate system to suppress the third harmonic. Finally, an experimental platform based on FPGA is developed to compare the proposed strategy with the traditional hysteresis algorithm and the large vector SVPWM algorithm, and analyze the influence of the three algorithms on the phase current ripple and harmonic content, thus verifying the correctness and superiority of the proposed algorithm.