A speed estimation scheme based on the back electromotive force (back-EMF) of motors was developed for a direct torque control (DTC) permanent magnet synchronous motor (PMSM) drive. The DTC PMSM drive was established using stator flux and electromagnetic torque. Three-phase stator currents and voltages were utilized to develop a rotor position estimator on the basis of back-EMF. The estimated rotor speed was derived from the rotor position estimator. Hall effect current sensors were used as an electromagnetic sensing element to obtain the stator current from the DTC PMSM under loading. Voltage space vector pulse width modulation (VSVPWM) was utilized to establish a voltage source inverter (VSI) in place of the traditional switching table (ST) VSI to reduce the ripples of the stator current and electromagnetic torque. A speed controller was designed using a modified particle swarm optimization (PSO) algorithm to achieve rapid convergence, low operational cost, and good applicability under various conditions. The MATLAB/Simulink© toolbox was used to establish the simulation scheme, and all the control algorithms were realized on a control card (Texas Instruments TI DSP 6713-and-F2812). Simulation and experimental results (including the estimated rotor speed, stator current, estimated electromagnetic torque, and stator flux locus) confirmed the effectiveness of the proposed approach.