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Data grids deal with a huge amount of data regularly. It is a fundamental challenge to ensure efficient accesses to such widely distributed data sets. Creating replicas to a suitable site by data replication strategy can increase the system performance. It shortens the data access time and reduces bandwidth consumption. In this paper, a dynamic data replication mechanism is proposed, which is called Latest Access Largest Weight (LALW). LALW selects a popular file for replication and calculates a suitable number of copies and grid sites for replication. By setting a different weight for each data access record, the importance of each record is differentiated. The data access records in the nearer past have higher weight. It indicates that these records have higher value of references. In other words, the data access records in the long past have lower reference values. A Grid simulator OptorSim is used to evaluate the performance of this dynamic replication strategy. The simulation results show that LAHW successfully increases the effective network usage. It means that the LALW replication strategy can find out a popular file and replicates it to a suitable site.