In order to expand the speed range for an indirect matrix converter–surface mounted permanent magnet synchronous motor drive (IMC-SPMSM), a wide speed range operation control strategy based on a flux-weakening control and an over-modulation method is proposed in this paper. In the stage of the inverter, an IMC over-modulation method is designed, which increases the fundamental voltage transmission ratio (VTR) to 1. In addition, considering the variation of the voltage limit boundary of the IMC with motor speed, flux-weakening control is implemented based on the voltage error feedback method, which maximizes the voltage utilization rate by setting the endpoint of the output voltage vector on the voltage boundary during the flux-weakening operation. In the stage of the rectifier, over-modulation is automatically switched on or off according to operation requirements by a modulation depth controller. Finally, experimental results show that the proposed strategy increases the maximum speed of the IMC-SPMSM by nearly 35% compared to the maximum torque per ampere (MTPA) method. Besides, the enlarged voltage margin by the rectifier stage over-modulation effectively shortens the setting time.