[Objective] To solve the parameter mismatch problem of model predictive current control (MPCC) for permanent magnet synchronous motor (PMSM), incremental MPCC with model reference adaptive system (MRAS) is used for parameters identification in order to improve the parameter robustness of the control system. [Methods] Firstly, the MPCC system based on the incremental model was established to eliminate the flux linkage parameter, and the parameter sensitivity of the incremental MPCC model was also analyzed, in which the resistance parameter mismatch had a small and negligible influence on the current prediction effect. Therefore, based on the dq-axis current, MRAS was used to identify only the dq-axis inductance, thus avoiding the under-rank problem. [Results] Simulation analysis and real-time verification were carried out based on Matlab/Simulink and STM32 platform. The results showed that MRAS could accurately identify the dq-axis inductance parameters. And although the incremental MPCC and MRAS control models need to set the resistance parameter, the mismatch of the resistance parameter had less impact on the identification results of the dq-axis inductance. The added MRAS parameter identification system did not additionally increase the large computational burden, and it had a better real-time performance. [Conclusion] For the four parameters of dq-axis inductance, flux linkage and resistance of PMSM, the incremental MPCC eliminates the flux linkage parameter, while the resistance parameter does not need to be identified precisely, and only the dq-axis inductance need to be identified by MRAS. The mismatch of the resistance parameter of the MRAS control model and the incremental MPCC has no effect on the control performance, which effectively improves the MPCC parameter mismatch robustness of PMSM.