When renewable energy sources using virtual synchronous generator (VSG) technology experience output fluctuations, adaptive inertia damping control can suppress the additional oscillations in output power and frequency caused by the inherent dynamic response of the VSG. However, existing VSG adaptive control strategies based on radial basis function (RBF) lack control flexibility and involve complex parameter configuration, making them ineffective at restraining output power and frequency oscillations under continuous output fluctuations. To address this issue, a VSG adaptive inertia damping control strategy is proposed, in which particle swarm optimization (PSO) is used to optimize the RBF neural network. First, a small-signal model of the VSG is established, the range of values for virtual inertia and virtual damping are determined, and the steady-state inertia is set. Then, an RBF neural network is utilized to fit the relationship between the VSG’s angular frequency and its virtual inertia and damping, and a J-inertia factor is introduced to expand the control dimension of the RBF neural network. Furthermore, an improved PSO algorithm is applied to optimize the hyperparameters of the RBF neural network, enhancing its fitting and generalization capability so that it can perform adaptive inertia damping regulation under complex power and frequency fluctuations. Finally, a VSG grid-connected model is established, and the feasibility and superiority of the proposed control strategy are verified under three operating conditions: sudden output change, continuous output fluctuations and different grid conditions.