In this paper a novel contention resolution scheme, namely Expanded Priority Vector (EPV) approach is proposed to support differentiated Grid service over OBS networks. EPV is an enhancement to a previously proposed application-aware contention resolution scheme for the OBS-based-Grid services in the literature. By using the EPV we keep all the advantages of the application-aware contention resolution. Moreover, we introduce fairness among the contending jobs of the same class by taking care of the two least significant digits of the vector. Those two digits pay attention to the remaining distance to the resource and the job size. By simulations, we show that EPV based policy reduces the blocking probability for all classes of submitted jobs.