Due to the complexity of Grid computing, many new security problems have appeared in grid, and so the traditional network security practices can not meet the security demand of grid. As a result, the study of security problems in grid is important, complicated and arduous. In this paper, we propose a new approach to construct grid security systems, and analyze both the disadvantages of current existing grid security systems. Our grid security system framework is positioned as an alternative to the security framework of Open Grid Service Architecture (OGSA). Based on our analysis, we conclude that a security system in grid should be composed of two parts: security rule definitions and security rule implementation. We also discuss the advantages of our new security system architecture.