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Distributed job scheduling does not incorporate a single point of failure in the system. In this algorithm, an ant is invoked in response to submitting a job to the Grid and this ant surfs the network to find the best resource to deliver the job to. We have carried out simulation of our proposed approach using a Grid job scheduling simulation toolkit (Alea) built upon Gridsim dedicated to Grid simulations. The performance of the algorithms will be evaluated using several performance criteria (e.g. makespan and average turnaround time). A comparison of our proposed approaches with a classical approach will also be provided. Analysis of experimental results shows that the proposed algorithm can perform better as compared to other approach in a Grid environment.