Grid voltage feedforward is extensively used for controlling grid-connected converters. However, the conventional voltage feedforward control reduces the stability margins of the converter connected to a high-impedance grid. The effect mechanism of voltage feedforward on the grid-connected converter control under high-inductive conditions of the grid impedance is clearly explained in this study using the equivalent transformations of control block diagrams. Results show that the delay produced by the digital control is the root cause of this effect. An improved voltage feedforward strategy, in which a bandpass filter (BPF) is introduced into the feedforward path, is proposed to strengthen the converter's robust stability against grid impedance variations. The selection method of the BPF's bandwidth is also provided considering the tradeoff between the response speed to the grid voltage sag and the system's robust stability. The converter can work stably over a wide range of the grid impedance through the proposed approach. Simulation and experimental results fully verify the effectiveness of the BPF-based voltage feedforward strategy.