The main drawbacks of traditional finite set model predictive control are high computational load, large torque ripple, and variable switching frequency. A less complex deadbeat (DB) model predictive current control (MPCC) with improved space vector pulse-width modulation (SVPWM) under a single-phase open-circuit fault is proposed. The proposed method predicts the reference voltage vector in the α-β subspace by employing the deadbeat control principle on the machine predictive model; thus, the exhaustive exploration procedure is avoided to relieve the computational load. To perform the constant switching frequency operation and achieve better steady-state performance, a modified SVPWM strategy is developed with the same conventional structure, which modulates the reference voltage vector. This new approach is based on a redesigned and adjusted post-fault virtual voltage vector space distribution that eliminates the y-axis harmonic components in the x-y subspace and ensures the generation of symmetrical PWM pulses. Meanwhile, the combined merits of the DB, MPCC, and SVPWM methods are realized. To verify the effectiveness of the proposed control scheme, comparative experiments are performed on a five-phase permanent magnet synchronous motor (PMSM) drive system.