The conventional finite control set-model predictive control (FCS-MPC) suffers from poor robustness against model mismatches. This paper presents an improved FCS-MPC with a reconstructed mathematical model to predict current variations without using a lookup table (LUT) or motor parameters. The model coefficients and current variations related to different voltage vectors can be updated during each control period. As a result, the prediction error is significantly reduced at low switching frequency when compared with the prior LUT-based model-free predictive current control (MFPCC). Additionally, the tracking accuracy of the proposed method at high speeds is improved due to the elimination of approximation error. Furthermore, a simple scheme is developed to suppress neutral-point-potential drift without knowledge of the dc-bus capacitor. Simulation and experimental tests, along with comparisons with prior arts carried out on a three-level inverter-fed surface-mounted permanent magnet synchronous motor drive, confirm the superiority of the proposed method.