To eliminate the influence of motor parameter mismatch on finite control set model predictive current control (FCS-MPCC), a parameter robust FCS-MPCC for surface permanent magnet synchronous motor (SPMSM) drives is proposed. First, the incremental prediction model (IPM) is introduced, which eliminates the flux linkage parameter; moreover, the parameter sensitivity analysis shows that the influence of resistance parameter mismatch on IPM can be ignored. Second, an inductance information extraction strategy is proposed, which can extract the actual inductance information according to the current prediction errors of IPM. Therefore, the proposed FCS-MPCC based on IPM is robust to all motor parameters. In addition, to ensure the correctness and stability of the inductance information extraction strategy, a parameter update mechanism is introduced, in which the inductance information is updated only when the switching states of the first two control periods are different. Finally, the comparative simulation and experiments are carried out, and the results show that the proposed FCS-MPCC is not influenced by the mismatch of any motor parameters and always has better current tracking performance than traditional FCS-MPCC.