Recent trends in the utilization of renewable and sustainable energy sources have led to an increased penetration of inertialess power electronics-based energy resources into the electrical grid. The concept of the virtual synchronous generator (VSG) has recently been studied to overcome the drawbacks of the fast-responding inertialess inverter by mimicking the behavior of a traditional synchronous generator. The majority of literature on VSGs assumes the operation of VSGs in inductive networks; however, such control algorithms do not operate well in a more resistive network such as a low-voltage distribution network. This article introduces a new neural network-based predictive control for VSGs that is capable of operating optimally in both inductive and resistive networks by optimizing the total tracking error during transients. After the introduction of the control scheme, simulation and experimental results are provided to evaluate the effectiveness of the proposed algorithm in reducing oscillations and settling time.