[Objective] To address the transient stability challenges in grid-following and grid-forming (GFL-GFM) converters parallel system, this paper proposes a transient stability control method based on dynamic adjustment of inertia-damping. [Methods] Firstly, a two-stage transient control framework was established for the GFL-GFM converters parallel system. During the fault period, fault current limiters were rapidly activated to mitigate overcurrent, while in the post-fault recovery stage, the phase-locked loop (PLL) of GFL converter and the inertia-damping parameters of GFM converter were dynamically adjusted. Secondly, the Sigmoid function was adopted to achieve inertia-damping coordination tuning, and the controller parameters were adaptively adjusted by the trend of the power angle of the parallel system. Finally, a time-domain simulation model of the parallel system of GFL-GFM converters was established based on the Matlab/Simulink platform. Through comparisons with traditional control methods and tests under voltage sag conditions of varying degrees, the effectiveness of the proposed transient control method was verified from multiple aspects. [Results] The results showed that compared with the traditional PLL freezing of GFL converter and the additional power control strategy of GFM converter, the proposed control method significantly reduced the amplitude of the power angle oscillation of GFL-GFM converters, greatly shortened the oscillation period, and adapted well to both mild and severe voltage sag conditions. The proposed control method effectively ensured the transient stability of the GFL-GFM converters parallel system during the whole fault process, and it also reduced the power angle oscillation deviation by more than 5%. [Conclusion] The proposed method enhances the adaptability and robustness of GFL-GFM converters parallel system under voltage sag of varying degrees, providing a new idea for the stable operation of grid-connected system with high proportion of power electronic equipment, which has good application value.