To improve the performance of three-phase voltage source pulse-width modulated (PWM) rectifiers (VSR) under unbalanced grid voltage conditions, a fixed-frequency current predictive control (CPC) strategy is presented. Instantaneous power of the three-phase VSR is analysed in a two-phase stationary frame. The calculation method for the reference current is improved to achieve the power stability at the AC side of the rectifier. Based on the current predictive model, the optimal duration of the voltage vectors is computed under the restricted condition of minimizing current error at α- and β-axes in fixed intervals. The control system is free of synchronous rotation coordinate transformation, and avoids positive and negative sequence decomposition, which simplifies the calculation. The simulation and experimental results show that the proposed control strategy is able to eliminate the AC current distortion effectively and depress DC link voltage fluctuation under unbalanced grid voltage. Furthermore, the control strategy has faster dynamic response ability, enhancing the control performance of the three-phase VSR system.