New challenges are introduced when people try to build a general-purpose mobile agent middleware in Grid environment. In this paper, an instance-oriented security mechanism is proposed to deal with possible security threats in such mobile agent systems. The current security support in Grid Security Infrastructure (GSI) requires the users to delegate their privileges to certain hosts. This host-oriented solution is insecure and inflexible towards mobile agent applications because it cannot prevent delegation abuse and control well the diffusion of damage. Our proposed solution introduces security instance, which is an encapsulation of one set of authorizations and their validity specifications with respect to the agents specific code segments, or even the states and requests. Applications can establish and configure their security framework flexibly on the same platform, through defining instances and operations according to their own logic. Mechanisms are provided to allow users delegating their identity to these instances instead of certain hosts. By adopting this instance-oriented security mechanism, a Grid-based general-purpose MA middleware, Everest, is developed to enhance Globus Toolkits security support for mobile agent applications.