The self-synchronizing voltage source inverter (SSVSI) is widely studied because of its grid-forming capability. However, the slow response of the active power control loop (APCL) under the weak grid makes it difficult for the SSVSI to quickly support the frequency of a low-inertia grid. In this paper, a grid framework is established to analyze the frequency support service process of the SSVSI, and the shortcomings of the regulation of the damping coefficient and virtual inertia coefficient for frequency support are analyzed. Then, an adaptive additional damping control method is proposed to optimize the ability of SSVSI to support the grid frequency. The proposed control method adjusts the damping of the APCL without affecting the system steady-state characteristics, which improves the active power response speed of the SSVSI. Besides, the proposed control method adaptively adjusts the additional damping coefficient based on the active power response without measuring the grid parameters. Compared with other forms of control, the proposed control method excels in minimizing the rate of change of frequency (RoCoF) and the frequency deviation (FD) within the grid, without succumbing to the constraints posed by unknown grid parameters. Furthermore, the analysis of the system stability is also presented. Finally, the experimental hardware results obtained from a miniaturized grid prototype are presented, corroborating the effectiveness of the proposed control method.