To solve the problem of unsuitable inertia and weak robustness of the model predictive control (MPC) for the motor driving system on electrical vehicles (EVs), an adaptive inertia observer-based model-free predictive current control (MF-PCC) strategy is proposed in this paper, and applied to the permanent magnet synchronous motor (PMSM) driving system to adjust the system inertia online. The current load of the EV is converted to the mass and load inertia, and an adaptive inertia method is designed to realize the inertia match between system inertia and load inertia based on online estimated load torque. Control performances of this method are analyzed in principle by bode diagrams and zero-pole maps with different sampling periods and inertia ratios. The effectiveness and correctness of the proposed method are demonstrated according to the experimental results compared with MF-PCC with fixed inertia and conventional PCC strategy. The advantages of better dynamics and current quality with suitable robustness and stability are accomplished by adaptive inertia.