Data deduplication (dedupe for short) is a special data compression technique. It has been widely adopted to save backup time as well as storage space, particularly in backup storage systems. Therefore, most dedupe research has primarily focused on improving dedupe write performance. However, backup storage dedupe read performance is also a crucial problem for storage recovery. This paper designs a new dedupe storage read cache for backup applications that improves read performance by exploiting a special characteristic: the read sequence is the same as the write sequence. Consequently, for better cache utilization, by looking ahead for future references within a moving window, it evicts victims from the cache having the smallest future access. Moreover, to further improve read cache performance, it maintains a small log buffer to judiciously cache future access data chunks. Extensive experiments with real-world backup workloads demonstrate that the proposed read cache scheme improves read performance by up to 64.3%.