LCL-type grid-connected inverters have been widely used for distributed generation. There is a stability issue caused by weak grid conditions, especially when the equivalent grid impedance varies in a wide range. Sliding mode control, as a typical nonlinear robust control, has been applied and proved to be effective. However, because of its special control law design, the controller requires multiple state variables to feedback, thus increasing the number of sensors. Due to this, this paper presents an observer-based discrete sliding mode control strategy. The state observer can observe state variables and predict the next step. By combining state observer with discrete sliding mode control, the system can reduce the number of sensors without affecting the control effect. In order to provide further stability margin, a PR controller and capacitor voltage active damping are designed. This paper develops a detailed design progress and stability analysis to complete the control scheme. The theoretical analysis and results verified through computer simulations show good performance.