A three-phase three-wire LCL grid-connected inverter is usually used as an interface between renewable-energy sources and grid. However, grid voltage is always distorted and results in grid-current distortion when there is no control at the filtercapacitor current. This paper presents the grid-current improvement with inverter-side-current direct digital control and capacitor voltage feedforward (CVF) for the grid-connected inverter under distorted grid voltages. With the inverter-side current feedback, the simple direct digital control can cover inductance variation and determine the control laws to track inverter-side inductor current, achieving robustness. A hysteresis repetitive predictor with finite impulse response low-pass filter and compensator term is introduced to the CVF loop which can stabilize the system and compensate the distorted grid current. The virtual impedance method is adopted to confirm the stability when the filter inductances drop and control parameters vary with the inductor current. Simulated and experimental results from 12 kW inverter are used to verify the theoretical analyses and discussions.