Grid computing provides a virtual framework for controlled sharing of resources across institutional boundaries. Recently, trust has been recognized as an important factor for scheduling in Grid. Trust is a complex subject relating to such as reliability, honesty, and competence of the trusted entity. Trust value computing becomes more difficult in Grid as the nodes are independent and distributed, and with a securityaware task execution model, task scheduling is crucial to achieving high performance. In this paper, we present a trust model wherein each node is assigned a trust value that reflects the transaction experiences. Eigenvector is used to calculate the trust value and distribute eigentrust algorithm is modified according to the characteristic of the Grid. Furthermore, trust managers are set to guide scheduling, and securitydriven algorithms are proposed to ensure the security of the executions. Simulations are performed to evaluate the performance of the algorithms.