Built on Internet and World Wide Web, the Grid is a new class of infrastructure which supports coordinated resource sharing and problem solving in dynamic, multi-institutional virtual organizations. In a grid architecture, a grid workflow management system is a type of user-level grid middleware. It aims to support large-scale sophisticated scientific and business processes in a variety of complex e-science and e-business applications. Such sophisticated processes are modeled or redesigned as grid workflow specifications at build-time stage by some modeling languages such as Grid Workflow Execution Language (GWEL), Abstract Grid Workflow Language (AGWL), and Martlet. The specifications normally contain a large number of computation, data and/or transaction intensive activities. Then, at run-time instantiation stage, grid workflow instances are created. Finally, at run-time execution stage, grid workflow instances are executed by facilitating the super computing and data sharing capability of underlying grid infrastructure to complete the computation, data and/or transaction intensive activities.