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In this paper, we propose an adaptive data replication algorithm, called the Popular File Replicate First algorithm (PFRF for short), which is developed on a star-topology data grid with limited storage space based on aggregated information on previous file accesses. The PFRF periodically calculates file access popularity to track the variation of users' access behaviour behaviors, and then replicates popular files to appropriate sites to adapt to the variation. We employ several types of file access behaviors, including Zipf-like, geometric, and uniform distributions, to evaluate PFRF. The simulation results show that PFRF can effectively improve average job turnaround time and data availability as compared with those of the tested algorithms.