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Virtual synchronous generators (VSGs) are widely introduced to the renewable power generation, the variable-speed pumped storage units, and so on, as a promising grid-forming solution. It is noted that VSGs can provide virtual inertia for frequency support, but the larger inertia would worsen the synchronization stability, referring to keeping synchronization with the grid during voltage dips. Thus, this paper presents a transient damping method of VSGs for enhancing the synchronization stability during voltage dips. It is revealed that the loss of synchronization (LOS) of VSGs always accompanies with the positive frequency deviation and the damping is the key factor to remove LOS when the equilibrium point exists. In order to enhance synchronization stability during voltage dips, the transient damping is proposed, which is generated by the frequency deviation in active power loop. Additionally, the proposed method can realize seamless switching between normal state and grid fault. Moreover, detailed control design for transient damping gain is given to ensure the synchronization stability under different inertia requirements during voltage dips. Finally, the experimental results are presented to validate the analysis and the effectiveness of the improved transient damping method.