The Agent in Grid (AiG ) project aims to develop an agent-based infrastructure that facilitates the resource management in the Grid. The core assumptions behind the system are: software agents representing Grid resources work in teams, and all information is ontologically represented and semantically processed. Thus far, trust management in AiG system is approached from the perspective of breaching an agreement between Users and teams or contracts between teams and Workers. Unfortunately, it is also possible that some Workers, which fulfilled the agreement, could have maliciously returned incorrect results from the jobs that they executed. In this paper, we discuss how the trust management in the AiG project can be improved by using a reputation-based voting technique, in order to assure reliable job execution.