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Meeting users' deadline constraint is usually the most important goal of workflow scheduling in Grid environment. In order to consider the dynamism of Grid resource, we adopted a stochastic model to describe dynamic workloads of Grid resources. A concept called Deadline Satisfaction Degree of Workflow (DSDW) was defined to represent the probability that a workflow could be completed before its deadline. We calculated task execution priorities based on their precedence relations in the workflow, then determined the candidate resource for each task so as to maximize DSDW, finally converted distribution problem of overall workflow deadline into a nonlinear programming problem with constraints and resolved it with known solutions. A Deadline Satisfaction Enhanced Scheduling Algorithm for Workflow (DSESAW) involving deadline distribution and resource selection was presented. The extensive simulation experiments using a practical medical image analysis application was conducted to verify our algorithm. Experimental results indicated that our algorithm could adapt to dynamic Grid environment and provide a good guarantee for user's deadline requirements.