In the grid-connected inverter based on the deadbeat current control, the filter inductance variation and one-step-delay control delay affect the distortion of the grid current, stability and dynamic response speed of the system. In this paper, a deadbeat grid-connected control method based on robust PWM is proposed, which reduces the distortion of the grid current caused by the filter inductance variation, effectively solves the delay of the one-step-delay control, reduces the characteristic root equation order of the closed-loop transfer function of the system, and improves the stability and dynamic response speed of the system. The influence of the filter inductance deviation coefficient on the system performance is analyzed, and the filter inductance deviation coefficient of the system critical stability increases with the increase of the parasitic resistance of the filter inductance and the line equivalent resistance and decreases with the increase of the sampling frequency. Considering the stability and dynamic response speed of the system, the optimal selection range of the key control parameters is given. Simulation and experimental results verify the effectiveness of the proposed method.