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Data replication can be used to reduce bandwidth consumption and access latency in the distributed system where users require remote access to large data objects. In this paper, according to the intrinsic characteristic of distributed storage system, the parallel replication algorithm NBPRA (Network-Bandwidth-based Parallel Replication Algorithm) is proposed. In the NBPRA, according to the network state, several replicas of a data object are selected, which are of the least access cost; then the different parts of the data object are transferred from these replicas, and they are used to make a new replica. The results of performance evaluation show that the NBPRA can utilize the network bandwidth efficiently, provide high data replication efficiency and substantially better access efficiency, and the improvement of system performance is related to the number of different data objects accessed by jobs.