Abstract--Scheduling algorithm for batch-mode dataintensive jobs is a key issue in data-intensive Grid applications. It focuses on how to minimize the overhead of transferring the required data set to the executing grid site. Existing approaches pay attention to the access cost of a data-intensive job at each executing grid site for replicating the required data set. However, they neglect the influence from potential behaviors of jobs in the waiting queue at each grid site when the access cost is evaluated. In this paper, we consider the influence of potential behaviors on the access cost, and propose a data-intensive job scheduling algorithm with potential behaviors. Furthermore, the causation of potential behaviors is analyzed. The simulation result in OptorSim shows that it has better performance in mean job time of all jobs, total number of replications, total number of local files accesses and effective network usage than the scheduling algorithm based on access cost.