This paper proposes a model predictive control （MPC） method for permanent magnet synchronous motors （PMSMs） based on finite control set Gaussian process MPC （FCS-GPMPC） parameter identification to limit the influence of model mismatches on the control system and to improve the current controller performance of control systems in a PMSM. First， the current PMSM prediction model is introduced and the influence of model parameter mismatches on the system performance is analyzed. Secondly， in order to simplify the complex debugging process of hyperparameters in general machine learning parameter identification algorithms， the GPMPC method is proposed. At the same time， the confidence interval of the predicted value is introduced as a real-time evaluation reference for the parameter prediction effect. Finally， the GP parameter identification method is combined with the FCS-MPC to predict the system current after accurately obtaining the identified parameters. The model is updated to improve system robustness and current loop tracking performance. The experimental results show that under the statistical characteristics of the training data， the root mean square error and of the test data are 0.0021 and 0.99， respectively. Under the condition of parameter fluctuation， compared with FCS-MPC， FCS-GPMPC reduces current fluctuation by 30.5% and the average current offset by 19.6%. In addition， for step changes in the reference current， FCS-GPMPC has a better dynamic response. The proposed GP-MPC can effectively suppress the influence of model mismatch on control systems and can improve the performance of the current controller of PMSM control systems.