The emergence of scientific applications that produce huge volume of data files requires special attention, and leads to the problem of how to manage and share such data files in wide area properly. In large-scale Grid, data replication provides a suitable solution for managing data files where data reliability and data availability are enhanced. Replica selection is one of the major functions of data replication that decides which replica location is the best for Grid users. In this paper, we address the replica selection problem in a Grid environment where the users are competing for the limited data resource. Thus, our aim is to establish fairness among the users in the selection decisions. Since the criteria that play a role in the selection process conflict with each other and produce heterogeneous values, the Analytical Hierarchy Process is used to solve this optimization problem. The proposed system validity and performance are evaluated by using a simulation. The simulation results were produced and discussed in this paper.