Data replication is a promising technique to increase access to performance and data availability in Data Grid (DG) systems. Current work on data replication in Grid systems focuses on infrastructure for replication,and mechanisms for creating or deleting replicas.The problem to determine minimum number or replicas as well as their locations in DG has not been studied, well enough. In this paper , we propose an algorithm formulated by using dynamic programming-based algorithm to find Optimal Number of Replicas (ONR) of a dataset over DG systems, so that the read cost (i.e. transferring object over the data Grid systems to the end-user) and the cost of storage (i.e. site building cost) can be minimized.We have also proposed a sketch of the proof for our algorithm and its integrity.