This paper analyzes the requirement of authorization service for Grid Computing Systems and proposes the use of threshold closure as a basic mechanism for implementing authorization service in Grid Computing Systems. While pointing out the desirable features of threshold closure for complex authorization policies, the paper also discusses the practical limitations of threshold closure in such an environment, and then puts forward a new authorization service for Virtual Organization. In addition, an access control protocol which is based on PKI is designed in the paper. By segregating the policy and mechanism aspects of threshold closure, the new service can use existing security infrastructure in Grid Computing System while keep the ability to express complex authorization policy effectively.