With the expansion of user scale in LEO satellite networks, unbalanced regional load and bursty network traffic lead to the problem of load disequilibrium. A distributed hops-based back-pressure (DHBP) routing is proposed. DHBP theoretically derives a fast solution for the minimum end-to-end propagation hops between satellite nodes in inclined-orbit LEO satellite networks; hence, link weights are determined based on remaining hops between the next hop and destination satellites. In order to control the number of available retransmission paths, the permitted propagation region is restricted to a rectangular region consisting of source-destination nodes to reduce the propagation cost. Finally, DHBP is designed distributedly, to realize a dynamic selection of the shortest link with low congestion and balanced traffic distribution without obtaining the whole network topology. Network simulation results demonstrate that DHBP has higher throughput and lower delay under high load conditions compared with state-of-the-art routing protocols.