This paper proposes a simplified and improved model predictive current control (MPCC) scheme for grid-connected bidirectional voltage source converter (GC-BVSC) when the unbalanced grid voltages occur. In conditions of unbalanced grid voltage, the current harmonic components of the GC-BVSC increase significantly, and twice grid-frequency ripple exist in both active power and reactive power, which influence the output power quality. To reduce harmonic currents and power fluctuations, an improved MPCC (IMPCC) method is proposed, and a two-step predictive model of GC-BVSC is put forward. The current compensation values are expressed by grid voltages and their quadrature signals that lag 90 electrical degrees in the alpha beta stationary coordinates system. The cost function reducing both the power ripple and current distortion is designed. Compared to conventional methods, phase-locked loop, pulse width modulation, and complex positive and negative sequence extraction of grid voltage are not required. In addition, IMPCC presents a better performance by reducing both grid-connected current harmonics and power ripple of GC-BVSC with flexible bidirectional power regulation capability. Simulation and experimental results on power electronics-professional (PE-PRO) platform verify the effectiveness of the proposed scheme under both single-phase and three-phase unbalanced grid voltages.