In weak grid environments, the larger grid impedance enhances the coupling between the grid and each inverter in a multi-inverter parallel system, resulting in decreased system stability or even instability. To address this, a strategy for improving the stability of multi-inverter grid-connected systems under weak grid conditions is proposed. Firstly, Norton equivalent models for single and multiple grid-connected inverters in weak grids are established. Secondly, from the perspective of grid-connected current stability, the stability criterion for the multi-inverter system is decoupled into that of a single-inverter system based on the concept of equivalent grid impedance, clarifying the mechanism behind the reduced system stability in weak grids. Subsequently, an improved control strategy to enhance the stability of the multi-inverter system is proposed, which increases the stability margin of grid-connected inverters by introducing an all-pass filter into the grid voltage feedforward loop and combines a harmonic controller to improve the system's ability to suppress background harmonics. Finally, simulation analysis verifies that the proposed strategy effectively enhances the stability of multi-inverter grid-connected systems under weak grid conditions.