Because of the powerful filtering ability the third-order LCL filters has been widely used in grid-connected inverters, but there are some problems to be solved on systems stability and control accuracy. A separated-PID control strategy has been proposed according to the PID characteristics and the structural features of a single-phase inverter connected to the grid with a LCL filter. This control strategy has some advantages as a strong dynamic tacking stability, and the system output has a small steady state error. A detailed description is presented on this control strategy applied in the single-phase grid inverter with a LCL filter. According to the Routh-Hurwitz stability criterion, the stability of a grid-connected inverter system based on the proposed control strategy has been analyzed. Finally, waveforms of this inverter have been presented through a simulation to show the steady and dynamic performance of the proposed scheme.