Despite the recent advances in access control approaches applicable to grid computing, there remain issues that impede the development of effective access control for grid applications. Amongst them are the lack of context-based models for access control, and reliance on identity or capability-based access control schemes. In this paper, we propose RCBAC model which extends the RBAC with context constraints. The RCBAC mechanisms dynamically grant and adapt permissions to users based on a set of contextual information collected from the grid environments, while retaining the advantages of RBAC model.