This paper proposes a grid synchronization control strategy for the grid-connected voltage source converters (VSCs) based on the voltage dynamics of the DC-link capacitor in the VSC. The voltage dynamics of the DC-link capacitor are used to regulate the frequency and phase angle of the inner potential of the VSC, synchronizing the VSC with grid. Firstly, in the proposed strategy, the active power regulation and grid synchronization of the VSC are combined, which are separated in the traditional control strategy. This can avoid the instability of the VSC in a weak grid with a low short circuit ratio (SCR), aroused by the dynamic interaction between the separated control loops in traditional control strategies. Secondly, the energy stored in the DC-link capacitor is directly coupled with the grid via the inner potential of the VSC, and the inertia characteristic is naturally featured in the inner potential by the proposed strategy. With the increase of the capacitance, the natural inertial response of the VSC is helpful to improve the grid frequency dynamic. Finally, simulation results are presented to validate the correctness and effectiveness of the proposed strategy on the enhancement of the grid frequency and voltage dynamic support capability.