In this study, a robust fault-tolerant predictive current control (RFT-PCC) algorithm based on a composite observer is proposed for permanent magnet synchronous motors (PMSMs), which can eliminate the influence of motor parameter perturbation and permanent magnet demagnetization. First, the effects of the parameter perturbation and permanent magnet demagnetization on the current vector are analyzed based on the conventional predictive current control. The composite observer based on the sliding mode observer and the Luenberger observer is then designed to observe the compensation voltage and current prediction value of the next time simultaneously. Finally, an RFT-PCC method is developed. The proposed RFT-PCC is able to effectively enhance robustness against parameter perturbation and permanent magnet demagnetization by adding compensation voltage. The current prediction value of the next time is used to replace the sampled current in RFT-PCC to compensate for the influence of the one-step delay. Comparative simulations and experimentations verify that the proposed RFT-PCC can improve the robustness while maintaining quick dynamic response of the current control loops.