Due to the significant difference in speed between the user terminals (UTs) and the low earth orbit (LEO) satellites, it is necessary to solve the frequent handover of UTs at the edge of the moving satellite beams. Besides, as the development of LEO satellite communications, the scale of constellations and the number of UTs undergoing massive increase. Thus, in this paper, a satellite handover strategy is proposed to improve the handover performances of UTs and satellites. We define the utility function of handover jointly by considering the quality of experience of UTs, the throughput of satellites and the load balancing of network. Then, a coding method is proposed to represent the combinations of UTs and satellites. To reduce the calculational cost, an access and handover strategy based on a heuristic algorithm is proposed to search the optimal handover result. Finally, simulations show the effectiveness and superiority of the proposed strategy.