LCL filters have greatly improved the current quality of grid-connected inverters, however, the problems of resonance and stability are also brought in inevitably. In this paper, feedback control methods with two different side inductance currents are studied and discussed, respectively. Based on feedback control method with grid side inductance current, the paper proposes a no damping control method, in which optimal designing of the ratio relationship between sampling frequency and resonance frequency are used in the digital control system. For another, while the system adopts the feedback control method with inverter side inductance current, a filter damping control method is proposed, where the resonant component extracted by an improved high-pass filter is adopted. Both of the two methods can avoid using any additional sensor in the main circuit, not only the design procedure is simple, but the reliability is high, and it is convenient for the engineering applications. At last, experimental results show that the theoretical analysis is correct and the control methods are feasible.