A robust incremental predictive current control algorithm is proposed to solve the dependence on motor parameters of the predicted current control for the permanent magnet synchronous linear motor. An incremental prediction model of the PMSLM is established to overcome the influence of the motor flux linkage variation, and the sensitivity of the incremental prediction model to the motor parameters is analyzed in detail. In order to improve the current bandwidth, one-shot delay compensation is performed for the incremental predictive current control. Considering the prediction error caused by the inductance mismatch, a new sliding mode observer is proposed to observe the voltage disturbance value. It is used as feedforward compensation, which can achieve precise current control. The experimental result shows that the proposed algorithm can effectively improve the robustness of the system and has a good effect. This work is supported by National Natural Science Foundation of China (No. 61573167) and the Fundamental Research Funds for the Central Universities (No. JUSRP51510).