It is a classic problem to judge whether there is a path between two vertices in a directed graph. For some practical applications such as routing and graph analysis, it is required to find whether there is a reachable path with limited hops, which is a variant of reachability query in graphs. For the query algorithm with limited hops on a large graph, it is necessary to balance the time and space efficiency of large-graph query and optimize the algorithm with the characteristics of limited hops. The common reachability query algorithm takes up too much space for small-degree vertex index entries, which leads to serious space waste. Therefore, we propose a hop-limited 2-hop partial index method, which combines an improved index method with local search to achieve hop-limited effective reachability query. The experimental results show that, compared with the existing algorithms, the proposed algorithm can save 32% index space and slightly increase query time on the Orkut social network dataset. Thus, the proposed algorithm can calculate the hop-limited reachability problem of larger graphs.