Satellite network has become an important supplement to the ground backbone network by the virtue of its wide coverage. Furthermore, satellite edge computing cluster can also provide real-time computing support for ground-based and space users. Focusing on the scenario where a task set consisting of multiple independent tasks which have high QoS requirements is offloaded to the satellite edge computing cluster, this paper establishes a model for transmission delay and calculation delay of computation delay, and proposes GASECO, a satellite edge computing offloading algorithm based on genetic algorithm. As shown in the simulation experiments, this algorithm improves the QoS of satellite edge computing services, shortens the response delay of task set, and reduces the failure rate of task offloading through the collaboration of satellite edge nodes.