Satellite edge computing has attracted the attention of many scholars due to its extensive coverage and low delay. Satellite edge computing research remains focused on on-orbit task scheduling. However, existing research has not considered the situation where heavily loaded satellites cannot participate in offloading. To solve this problem, this study first models the task scheduling of dynamic satellite networks as a minimization problem that considers both the weighted delay and energy consumption. In addition, a hybrid genetic binary particle swarm optimization (GABPSO) algorithm is proposed to solve this optimization problem. The simulation results demonstrate that the proposed method outperforms the other three baseline algorithms.