The model-free predictive current control based on the ultra-local model using predictor-based neural network (PNN) significantly reduces the sensitivity to the prior model parameters of the power converter. However, the performance of PNN degrades due to the amplified high-frequency disturbances caused by mismatched inductance parameters, especially when the inductance parameters are reduced. In order to address the aforementioned issue, in this paper an improved predictor-based neural network model-free finite set predictive control (IPNN-MFFSPC) for power converters is proposed. A fast and accurate method for estimating the inductance parameters is proposed based on discrete equations of the PNN. By compensating for inductance parameter disturbances, the robustness of the proposed method is further improved. Finally, simulations validate the effectiveness of the proposed method in handling inductance disturbances, confirming the strong robustness of the approach.