Grid Computing is concerned with the sharing and coordinated use of diverse resources in distributed Virtual Organizations. This introduces various challenging security issues. Among these trusting, the resources to be shared and coordinated with the dynamic and multi-institutional virtual organization environment becomes a challenging security issue. In this paper, an approach for trust assessment and trust degree calculation using subjective logic is suggested to allocate the Data Grid or Computational Grid user a reliable, trusted resource for maintaining the integrity of the data with fast response and accurate results. The suggested approach is explained using an example scenario and also from the simulation results. It is observed that there is an increase in the resource utilization of a trusted resource in contrast to the resource which is not trusted.