In this paper, a model-based current control strategy with virtual time constant is proposed for three-phase grid-connected LCL-filtered voltage source inverters. The proposed control strategy is based on controlling the inverter currents in the rotating dq frame by using current-oriented proportional-integral (PI) controllers rather than voltage-oriented PI. The PI controllers determine the inverter current references in the d- and q-axes by regulating the grid current. It is shown that the proposed strategy decouples the inverter current from other variables provided that the inverter-side inductance and its resistance values used in the control variable match the actual values in the system. In addition, the virtual time constant is introduced in the control variables to offer flexibility for adjusting the inverter current dynamics as desired. Moreover, the integral gain of PI controller has the ability to keep the LCL-resonance peak below 0 dB. Unlike the existing methods, the proposed strategy does not require a dedicated active damping. Computer simulations and experimental studies show that the proposed control strategy exhibits a good performance in achieving fast dynamic response and sinusoidal grid current with low THD under balanced, unbalanced, and distorted grid conditions.