The mathematical model of the three-phase grid-connected voltage source inverter（GC-VSI） is developed. Based on the model， a novel sliding mode variable structure（SMVS） based direct power control（DPC） strategy is proposed for the three-phase GC-VSI. The principle and design scheme of the proposed SMVS-DPC strategy is studied in detail. The proposed SMVS-DPC strategy combines SMVS controller， DPC method and space vector pulse width modulation（SVPWM） technique together to implement a constant switching frequency without involving any synchronous speed coordinate transformation. Thus it can achieve excellent steady-state performance as well as rapid dynamic response. Experimental tests are conducted on a 3 kVA three-phase GC-VSI and the results validate the correctness and feasibility of the proposed SMVS-DPC strategy.