This paper presents a model predictive control method with a controllable current spectrum applied to single phase grid-connected inverter. The method can predict the future value of the grid current by using the detection value of the current state based on the discrete-time model of a single phase grid-connected inverter; then takes the difference value between the predictive value and given value of grid current as a objective function, evaluates all voltage vectors and selects the voltage vector which minimizes the objective function; finally, uses the switch single deduced by the voltage vector to control the next output of single phase inverter, which can achieve the optimal control effect of grid current. In order to improve the frequency spectrum of grid connected current, a digital filter is added to the objective function. The method is easy to realize digital control and its physical model is distinct. It does not adjust the PI parameters and has a strong robustness compared with the traditional control method. The simulation results show that the controller has good tracking performance for grid current, and the control effect is similar to the constant switching frequency by current spectrum analysis.