In P2P Grid computing systems, the authorization decision is often tackled by two different trust management methods: policy-based approach, where authorization are built on logical rules and verifiable properties encoded in signed credentials, and reputation-based approach, based on collecting, aggregating and disseminating reputation among the peers. However, the overhead caused by proof of compliance on authorization and the absence of certifying authorities may negate the strong and objective security advantages of policy-based approach, whilst vagueness, complexity and inaccurate characterization caused by reputation evolution may eliminate the quantitative and flexible advantages of reputation-based approach. We propose an adaptive trust management framework, which combines the merit of policy proof and reputation evolution such that authorization is aware of not only the strong and objective security traits, but also the calculability and the availability security traits. Finally, the framework of system is proposed.