Frequency stability becomes more and more important with the increase in inverter-based resources in power systems. To enhance the frequency stability, this paper proposes a novel data-driven method for frequency stability assessment and control for energy storage systems (ESSs). Leveraging the neural ordinary differential Equation (ODE) framework, the method learns a continuous-time model of the system frequency dynamics. A neural-network-based controller is then designed according to the learned neural ODE model to enhance frequency stability. The training process involves an alternating optimization algorithm that updates both the neural ODE model and the controller parameters via the adjoint sensitivity method. Simulation results demonstrate that the proposed method accurately predicts frequency trajectories. Moreover, the designed controller reduces frequency deviation by 53%.