Satellite edge computing (SEC) has become a promising technology for future wireless networks to provide anywhere and anytime computing services. Different from terrestrial edge computing, the computing capacity at Low-Earth-Orbit (LEO) satellites is usually unstable, due to the limited and consistently changing energy supply of fast-orbiting LEO satellites. To well exploit the potentials of SEC, an optimal computation offloading strategy becomes imperative to determine when and how to offload computing tasks with respect to high dynamics of satellites. In this paper, we propose a dynamic offloading strategy to minimize the overall delay of tasks from terrestrial users in a SEC network, subject to the energy and computing capacity constraints of the LEO satellite. Based on Lyapunov optimization theory, a long-term stochastic problem with a time-varying energy constraint is converted into multiple deterministic one-slot problems parameterized by the current system state, where task offloading decisions, computing resource allocation and transmit power control are jointly optimized. Numerical results show that our algorithm achieves asymptotic optimality efficiently while maintaining the mean rate stable of the LEO satellite’s energy queue, and has a lower delay compared with the other two comparison approaches with acceptable energy consumption.