In this paper, a rerouting-controlled ISL (Inter-Satellite link) handover protocol for LEO satellite networks (RCIHP) is proposed. Through topological dynamics and periodic characterization of LEO satellite constellation, the protocol firstly derives the ISL related information such as the moments of ISL handovers and the intervals during which ISLs are closed and cannot be used to forward packet. The information, combined with satellite link load status, is then been utilized during packet forwarding process. The protocol makes a forwarding decision on a per packet basis and only routes packets to living and non-congested satellite links. Thus RCIHP avoids periodic rerouting that occurs in traditional routing protocols and makes it totally unnecessary. Simulation studies show that RCIHP has a good performance in terms of packet dropped possibility and end-to-end delay.