This paper presents robust predictive current control (RPCC) to achieve high current-loop performance for permanent magnet linear synchronous motor (PMLSM) drives. Firstly, a deadbeat current predictive algorithm is proposed and the predictive control model of PMLSM is derived. Secondly, the stability of the algorithm is analyzed and the stable condition of the algorithm is obtained. A robust control method is adopted to make the control algorithm stable in the range of motor parameter mismatch. Finally, physical experiments are carried out on the TMS320F28335 DSP experimental platform. Experimental results show the proposed algorithm has better dynamic performance and robustness. The correctness and effectiveness of the proposed method are verified by experimental results.