This paper proposes a routing scheme for multi-hop LEO satellite networks with inter-satellite links aiming for reducing the number of link handovers while keeping the efficient use of network resource. The proposed routing scheme controls the link handovers by taking account of the deterministic LEO satellite system dynamics, geographical location of a ground terminal and statistic information of call duration. The performance of the proposed routing scheme has been evaluated and compared with previous routing schemes in terms of average number of link handovers during a call, the call blocking and dropping probability, and the network utilization.