This paper addresses the problem of resource scheduling in a grid computing environment. One of the main goals of grid computing is to share system resources among geographically dispersed users, and schedule resource requests in an efficient manner. Grid computing resources are distributed, heterogeneous, dynamic, and autonomous, which makes resource scheduling a complex problem. This paper proposes a new approach to resource scheduling in grid computing environments, the hierarchical stochastic Petri net (HSPN). The HSPN optimizes grid resource sharing, by categorizing resource requests in three layers, where each layer has special functions for receiving subtasks from, and delivering data to, the layer above or below. We compare the HSPN performance with the Min-min and Max-min resource scheduling algorithms. Our results show that the HSPN performs better than Max-min, but slightly underperforms Min-min.