Although harmonics in AC side of a grid-connected voltage source inverter（VSI） can be filtered out with LCL filter better than with L filter， the three-order characteristic of LCL filter makes the system complicated and unstable. It is found that the power factor and power quality of the grid-connected VSI can be guaranteed only by direct grid-side current control， especially under the non-ideal grid condition. And at the same time， the arm current can be better limited to allowable value of power electronic block by arm current control of VSI， and it is in favor of effective operation of power electronic block. So a cascaded control strategy with multiple feedback loop， namely arm current of VSI， capacitor voltage and grid-side current， is designed in this paper. Meanwhile， in order to restrain the inherent system resonance and increase the damping ratio of LCL filter， a lead-lag element for active damping is added to the inner control loop of arm current of VSI. So a composite multiple feedback control strategy is achieved. Besides， the design method of multiple feedback loop control and the parameter selection of lead-lag element are discussed. The theoretical analysis and design scheme are verified by simulation and experiments on a 11 kW LCL-VSI system.