The min-projection strategy (MPS) is a switching rule with better convergence speed, which can improve the dynamic characteristics of three-phase grid-connected inverters. However, the grid-connected current harmonics of the system are large when the MPS is used directly in the digital control framework due to the limitations of the sampling frequency. To solve this problem, an improved min-projection strategy is proposed in this paper by introducing a zero voltage vector to the control. First, the non-zero voltage vector is selected through the switching law function of the MPS. Then the time occupied by the non-zero voltage vector and the zero voltage vector can be obtained through an error function, which is established by the principle of minimum current error. Finally, the switching signal can be obtained for control, based on the method of duty cycle modulation. This method can realize fast current tracking and current decoupling control, reduce the grid-connected current harmonics, and improve the steady state performance of the system without increasing costs. The effectiveness of the proposed method is verified by simulations and experimental results.