Computing systems are moving towards open, service oriented, dynamic and distributed architecture. In such an environment like grids support coordination of various resources that spans across multiple administrative domains. Diverse nature of grid resources introduces the challenge of establishing a trust between communicating entities. In this paper, the authors propose Trust Management System for computational grids. The mathematical model for the computing of trust value has been derived. The proposed system has been implemented and integrated with CARE Resource Broker (CRB). The impact of using trust in computational grids has been studied. The authors' system is beneficial in selecting the most reliable, trustworthy resources for the job execution that results in increased throughput of the resource broker.