Nowadays model based predictive control is widely used in grid-connected inverter current control, however, modeling accuracy is the key factor that affects its performance. In order to avoid the complex and time consuming modeling process, model free subspace based Linear Quadratic Gaussian (LQG) control strategy is proposed. Input and output measurements are utilized in the subspace predictor design, and then the predictor is used in model free predictive LQG control. This novel approach is applied to the grid-connected photovoltaic (PV) inverter control system. Simulation results show the inverter’s output current could comply with grid standards, which also verify good dynamical performance and strong robustness of the proposed method.