Grid-connected inverters are important components of distributed generation systems and microgrids. A grid-connected inverter topology with LC filter and isolation transformer is investigated. It has a high order mathematical model and is hard to control. Its reduced model is obtained by the definedvirtual feedback current”， which is useful for the controller design of proposed topology. Moreover， how the variable parameters affect the reduced model is studied in detail. According to the reduced model， a sliding mode variable structure control is designed. The correctness and effectiveness of the proposed approach is verified using PSCAD/EMTDC.