Grid infrastructures provide an environment for high performance computing by combining heterogeneous, widely distributed computational resources into a single cohesive computing infrastructure. One of the key goals of grid computing infrastructure is to provide an environment where users can share resources across heterogeneous domains. In such an infrastructure security is the major concern. Security itself is composed of various sub-issues like authentication, authorization, single sign-on, data integrity, confidentiality etc. Authorization deals with the issue like who is authorized to access which resource and under what condition i.e. controlling access to resources based on conditions. An authorization system must address different concerns like scalability, fine-grain access control, context based authorization, continuous decision enforcement. This paper proposes an authorization framework which addresses above issues in making access decision on the resource. This paper also discusses a prototype implementation of the framework and results show that framework is workable and addresses all issues related to authorization and access control.