[Objective] One-step and two-step model-free predictive current control (MFPCC) for permanent magnet synchronous motor (PMSM) system is established to address the strong parameter dependence issue in model predictive current control (MPCC). [Method] Based on the ultralocal model, one-step and two-step MFPCC for PMSM was implemented. The differential algebraic method was used to estimate uncertain parts of the first-order and second-order ultralocal models. The effect of the window sequence length of the ultralocal model on control performance was analyzed, along with the parameter robustness of the ultralocal model-based one-step and two-step MFPCC for PMSM with parameter variations. Real-time experiments were conducted to verify the results. [Results] Simulation and real-time experimental results showed that the window sequence length of the first-order ultralocal model significantly impacted the control performance. Increasing the window sequence length improved control performance until saturation. The window sequence length of the second-order ultralocal model had a smaller effect on control performance. The ultralocal model-based one-step and two-step MFPCC for PMSM showed strong parameter robustness with parameter variations. With the increase in window sequence length, the computational time for the ultralocal model increased slightly, but the overall real-time performance was minimally affected. [Conclusion] The ultralocal model-based one-step and two-step MFPCC for PMSM is feasible and demonstrates strong parameter robustness. The real-time performance of the ultralocal model-based one-step MFPCC is comparable to that of the conventional one-step MPCC. The ultralocal model-based two-step MFPCC exhibits slightly better real-time performance than the conventional two-step MPCC.