Abstract: Under mixed computing environment of grid and P2P(Grid & P2P), grid nodes provide the service with QoS guarantee. However, sharing computing resources of P2P no des is the user's volunteer action without QoS guarantee. The user is not respon sible for his actions. Therefore it's difficult to establish the trust relations hip among users with traditional trust mechanism. Referring to social people tru st relationship models, a grid & P2P trust model based on recommendation evidenc e reasoning is designed to solve the problem by building a recommendation mechan ism in Grid & P2P and integrating the recommendation evidence with the D-S theor y. Theoretical analysis and simulations prove that the model can tackle the trus t problem under Grid & P2P in a simple and efficient way.