In order to extend the connection time of the feeder link for dense LEO constellation and make full use of the resources of the gateway station, this article proposes a feeder link handover strategy for dense LEO constellation based on Hybrid Clonal Selection Algorithm. Firstly, the satellite-earth visible window is defined as an independent task, the link handover problem is transformed into a task assignment problem, and the corresponding mathematical model is established. Then, the task execution time window is calculated using the Conflict Resolution Algorithm, and the associated satellite coincidence time window is reassigned. Then, the Clonal Selection Algorithm is used for global search to complete the whole link handover. In order to enhance the local optimization ability of the algorithm, a Hybrid Clonal Selection Algorithm is proposed by combining the local search algorithm of adaptive neighborhood selection. Finally, the model is set up and the performance comparative analysis experiment is carried out. The experimental results show that the Hybrid Clonal Selection Algorithm can improve the task scheduling rate and extend the link connection time without sacrificing the link switching times.