In a Grid computing environment, each client has its own job represented as a workflow composed of tasks that require multiple types of computational resources to complete. Developing a mechanism that schedules these workflows to efficiently utilize limited amounts of resources in the Grid is a challenging problem. This paper takes a market-oriented approach allowing the job scheduling task to be distributed among clients. In this approach, several Workflow Agents plan a feasible schedule for their jobs and compete in the resource market. A Market Broker Agent is implemented to coordinate the conflicts in simultaneous access of the same resource. Experiment results show that the performance of the proposed approach surpasses those of first-come-first-sene and a variant of shortest-job-flrst method in terms of job completion ratio before deadline.