Current literature on indexing current and future positions of the moving objects lacks the mechanisms on concurrent access. To solve this problem, the current research proposed an efficient moving object index that supports concurrent access, also called CS²B-tree(Concurrent Space-filling curve enabled Cache Sensitive B⁺-tree). CS²B-tree combines the characteristics of the B^x-tree and CSB⁺-tree, thus it can support querying the predicted future positions of the moving objects and is cache sensitive. Focus was put on studying a concurrent access mechanism to CS²B-tree which resulted in a two-level lock mechanism and particularly a lock memo structure was designed. Based on the concurrent access mechanism, a CS²B-tree concurrent location update algorithm and a concurrent predicted range query algorithm were proposed respectively. Experimental results show that, compared with B^x-tree, the throughput of the CS²B-tree improves by 15.1%, and the response time decreases by 14.9%.