The model predictive control (MPC) methods for voltage source inverter (VSI) shows highly dependence on system parameters, and the performance degrades dramatically when the parameter mismatch happens. In contrast, model free predictive current control (MFPCC) can solve this problem with only the information of the measurement data. However, since the form of the conventional MFPCC for VSI consisting current difference term calculated by two adjacent sampling periods, the noise suppression ability of the conventional MFPCC method is incompetent. Therefore, this article proposes an improved MFPCC method, where an ultra-local model of VSI is established to replace the conventional MPC methods' mathematical model, and a Luenberger observer is adopted to estimate the disturbance term in ultra-local model to improve the regulation performance. In this way, the current difference term in traditional MFPCC can be avoided. Therefore, the proposed MFPCC method shows superior noise suppression performance capability compared to the conventional methods. Finally, the effectiveness of the proposed MFPCC method is verified through a series of simulation results.