With the rapid development of the power grid, more and more single- and three-phase grid-connected voltage source converters are demanded. This paper proposed a unified current control structure with complex vector form for both single- and three-phase grid-connected voltage source converter. The unified control structure can realize rapid design and convenient analysis of the single- and three-phase voltage source converter. The principle of the unification calculation and the complex resonators which are the two main parts of the current control are illustrated in detail. The single- and three-phase current control are unified as the same complex form operation. The control characteristics and parameter tuning methods are also analyzed and discussed in this paper. The detailed simulation results are used to verify the feasibility and correctness of the proposed control.