In permanent magnet synchronous motor drive systems, significant fifth- and seventh-order current harmonics are inevitably generated. This is caused by combined non-ideal factors such as the non-sinusoidal air-gap magnetic field of the motor itself, the inverter dead-time effect, and digital control delays. To overcome the limited control flexibility of traditional duty-cycle model predictive control in suppressing these harmonics, a duty-cycle model predictive control strategy is proposed in this paper. First, a method based on orthogonal projection mapping of space-vector voltages is proposed. By the principle of orthogonal projection, the two-dimensional fifth- and seventh-order harmonic compensation voltages are mapped to a one-dimensional coordinate. Thus, weighting coefficients in traditional multi-objective control are eliminated, and decoupling between fundamental and harmonic control is achieved. Next, a fifth- and seventh-order harmonic voltage compensation mechanism spanning control cycles is designed. This expands the controllable degrees of freedom of the duty-cycle model predictive control. Finally, experimental validation was conducted on a 5.5 kW permanent magnet synchronous motor in a dual-motor configuration. It is demonstrated by the results that the fifth- and seventh-harmonic currents and the total harmonic distortion are effectively reduced. The correctness and effectiveness of the proposed strategy are thus verified.