Replica placement is one of the important factors to improve performance in data grid systems. A good replica placement algorithm can result in good performance gains. It should be mentioned that, these algorithms or strategies are dependent on architecture of the data grid. By considering different kinds of architecture in data grid systems, a true representation of a grid is a general graph. So we propose a new algorithm for suitable placement of replicas on graph-based data grids. The performance of the proposed algorithm is improved by minimizing the data access time, avoiding unnecessary replications and nice performance in balancing the load of replica servers. The algorithm will be simulated using a data grid simulator Optorsim, developed by European Data Grid projects.