Voltage source converters (VSCs) are one of the most adopted power converter topologies in power electronic-based power systems. Over the years, various control strategies are introduced for grid-connected VSCs, aiming to provide high quality sinusoidal current generation, bidirectional power flow, robustness to uncertainties and mismatches, acceptable steady-state and dynamic performances as well as simplicity and low computational burden. To meet these goals, this paper proposes a direct adaptive current control strategy for three-phase PWM-VSC in grid-connected applications. In the proposed control method, a simple adaption law for updating the feedback control gains based on the Lyapunov stability theory is proposed, to compensate system uncertainties. The performance of the proposed control method is evaluated under various conditions by extensive simulation and experimental tests and show that the method is powerful and robust.