Abstract： Based on the mathematical model of the single-phase grid-connected inverter with LCL filter in discrete domain, the stability of the whole system was deeply investigated, considering the relationship between the sampling frequency and the resonant frequency of the LCL filter. The reason for the instability of the sampling frequency which is less than, equal to, and higher than the critical frequency, is discussed. The methods to reform the characteristics of the system were proposed. Two different digital filters were introduced to construct composite controller with the proportional resonant(PR) controller, and the system characteristics from the amplitude and phase was reformed respectively, making the whole system stable under low, medium and high sampling frequency with the composite controller. The validity of the analysis was assessed by both the numerical simulation and experimental results.