Trust has been recognized as important factor for Grid computing security. Trust is the degree of belief in the resource provider's competence to complete user's task dependably, securely and reliably in a specific context at a given time. In this paper, we propose the trust model in Grid system. It consists of Application Domain (AD), Client Domain (CD), Resource Domain (RD), and Trust Manager (TM). TM controls the relationship between RD and CD depending on trust level value of each client and classification of each resource. Trust level's values are from 0 (untrusted) to 1 (trusted). These values are changed to reflect the trust level of every client in every context. Performance metrics are makespan and utilization. We evaluated three batch mode scheduling algorithms. The experimental results show that the trust model can reduce makespan and can make little maximization of utilization. When we compare the conventional trust model and proposed trust model, the proposed trust model is better than the conventional trust model.