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Virtual Screening (VS), a productive and cost-effective technology in quest for novel lead compounds, is a new approach in the pharmaceutical industry. This kind of applications belongs to the family of large scale loosely coupled parallel applications, whereas concurrent tasks are independent of each other, and are most suited to run on the Grid environments. However, there are some important practical issues should be investigated, namely, the complicated scale of VS applications with diverse data sets, complexity of Grid Job Description Language and dynamic and heterogeneous grid environments. In this paper we propose a Comprehensive Task Management in the context of performing VS applications on Grid environments. First, we propose an extension of the Job Submission Description Language (JSDL) to specify the large scale data set packet strategy and a visual Task Editor to make the complexity of underlying task description transparent. Then we provide a coordinating mechanism to integrate multiple Grid platforms for VS applications. Furthermore, we present a task-level predictive model on estimating of execution time from historical information. Finally, we conduct a case study on discovering leads drug against Avian Influenza Virus H5N1 to highlight technical feasibility of our proposal.