With the growth of renewable energy and power electronic converters, the whole power system's moment inertia is decreasing. As a result, the synchronous generator control (VSG) technology is important. The VSG has a virtual constant moment inertia. However, the traditional VSG method faces many challenges, such as lag, instability and insensitivity. The need for advanced control methods to address these challenges has become increasingly urgent. In this paper, a new adaptive VSG (AVSG) control strategy is proposed. To get a more robust control, the AVSG strategy can adjust the droop coefficient and the inertia moment with the derivative of the ac-side frequency. The key parameters of the AVSG are obtained to improve the damping of the system according to the trajectory sensitivity method. A New England 39-bus benchmark system which connected to a multi-terminal high voltage direct current(VSC-MTDC) system is used to verify the efficiency of the proposed control strategy. The model was built in the DIgSIENT/Powerfactory software, and the proposed control has a good damping effect on the low frequency oscillations.