To track the sinusoidal current under stationary frame and suppress the effects of low-order grid harmonics, the multi-resonant quasi-proportional plus resonant (PR) controller has been extensively used for digitally controlled LCL-type pulse-width modulation (PWM) converters with capacitor-current-feedback active damping. However, designing the controller is difficult because of its high order and large number of parameters. Moreover, the computation and PWM delays of the digitally controlled system significantly affect damping performance. In this study, the delay effect is analyzed by using the Nyquist diagrams and the system stability constraint condition can be obtained based on the Nyquist stability criterion. Moreover, impact analysis of the control parameters on the current loop performance, that is, steady-state error and stability margin, identifies that different control parameters play different decisive roles in current loop performance. Based on the analysis, a simplified controller design method based on the system specifications is proposed. Following the method, two design examples are given, and the experimental results verify the practicability and feasibility of the proposed design method.