Under grid faults, the stability of the grid-connected inverter (GCI) system can be seriously threatened. Especially, under weak grid conditions, the high grid impedance will challenge the grid synchronization and the fault detection a lot. In this paper, by adopting the inverter-side current feedforward, the ideal voltage synchronization signal can be obtained and more accurate fault detection can be achieved because the voltage component across the grid impedance can be basically eliminated. Then, to tackle the challenge of grid voltage sag under very weak grid, a novel low-voltage-ride-through (LVRT) control strategy based on current feedforward is proposed. The simulation results have confirmed that the proposed LVRT strategy is effective to keep the stable operation of GCI system even when the short-circuit-ratio (SCR) is 1.3.