Thanks to their wide coverage and relatively low latency compared to geosynchronous satellites, Low Earth Orbit (LEO) satellite networks have been regarded as one of the most promising solutions to provide global broadband backhaul for mobile users and IoT devices. In LEO satellite networks, the frequent feeder link handover invokes unacceptable communication interruptions and affects the backhaul quality. To overcome this challenge, we propose a maximum backhaul capacity handover strategy for feeder links in LEO satellite networks. To improve the backhaul capacity, we design an available backhaul capacity ratio to jointly consider feeder link quality and the inter-satellite network in handover decisions. In addition, we introduce a service time factor and handover control factor to reduce the handover frequency. Then, we propose the handover utility function based on the designed handover factors and propose a greedy-based handover strategy. Simulation results show that the proposed strategy outperforms conventional handover strategies in backhaul capacity with low handover frequency.