Grid computing technologies enable widespread sharing and coordinated us of networked resources, including computing resources. Open Grid Service Architecture (OGSA) marries Web services to grid protocols, thereby making progress in defining interfaces for grid services. We put forward here a hierarchical architecture, which is based on grid service, for parallel computing in grid environment. Several grid services are proposed in this paper for building our architecture, including cooperation service, resource information service, computing service, communication service, and other atomic services such as MOM service. The technology of building high layer grid service is also introduced in this paper.