To address the inherent resonance issue of LCL grid-connected inverters， the optimized current control method and active damping method are proposed. To minimize the influence of digital system delays on current control and active damping， the deadbeat average model and compound delay elimination method are proposed. Because the control model is the basis of current control and time-delay compensation， a deadbeat average model for inverter-side current feedback control is established by introducing an oversampling method and incorporating signal processing method. This approach transforms the conventional single-sample instantaneous control into multi-sample average control， which improves the accuracy of the control model. Based on the established model， a predictive dead-beat average model （PDBAM） control method is proposed through the introduction of predictive control combined with the double-updated PWM method， which provides accurate delay compensation and improves the stability and robustness of the system. Based on PDBAM control， the average capacitor-voltage feedforward method is proposed， which eliminates the influence of digital delay on active damping and further strengthens the robustness of the system under weak grid conditions. The experimental results prove the effectiveness of the proposed method in this paper.