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Effective scheduling is a key concern for the execution of performance driven grid applications. In this paper, we propose a dynamic critical path (DCP) based workflow scheduling algorithm that determines efficient mapping of tasks by calculating the critical path in the workflow task graph at every step. It assigns priority to a task in the critical path which is estimated to complete earlier. Using simulation, we have compared the performance of our proposed approach with other existing heuristic and meta-heuristic based scheduling strategies for different type and size of workflows. Our results demonstrate that DCP based approach can generate better schedule for most of the type of workflows irrespective of their size particularly when resource availability changes frequently.