In order to solve the problem that the traditional Grid-Following (GFL) grid-connected inverter is prone to oscillation and instability under weak grid, a grid-following virtual synchronous mechanism construction and voltage feedforward control method based on the swing equation of the synchronizer are proposed. Firstly, the method refers to the Virtual Synchronous Generators (VSG) technology to derive and reconstruct the swing equation of the synchronous machine, and proposes a new voltage feedforward controller, which introduces inertia and damping to the control of the GFL inverter and improves the stability of the GFL inverter under the weak power grid. Then, the proposed control method is theoretically analyzed and optimized by establishing the frequency-coupling sequence admittance model, and the results show that the proposed method can significantly improve the negative resistance characteristics of the inverter in the middle and low frequency bands to enhance the stability of the GFL grid-connected inverter under the weak grid. Finally, this paper verifies that the proposed control method can operate stably in weak and very weak grids, as well as in strong power grids, which is of great significance for improving the adaptability and reliability of GFL grid-connected inverters in complex grid conditions.