The parallel operation of multiple inverters in weak grid environments intensifies coupling effects, leading to harmonic resonance that threatens grid stability and current quality. To address this, an improved capacitor voltage notch filter feedforward resonance suppression strategy is proposed, effectively mitigating harmonics in single and multi-inverter systems. Additionally, a BP-PID(Back Propagation Neural Network Proportional-Integral-Derivative) controller replaces the traditional PI(Proportional-Integral) controller, enabling real-time dynamic adjustment of control parameters to enhance dynamic response and steady-state performance under varying conditions. Simulink-based simulations validate the strategy, demonstrating significant improvements in harmonic suppression and system stability. This study provides a practical solution for harmonic mitigation and control optimization in multi-inverter systems under weak grid conditions.