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Task scheduling in Grid becomes more complicated when user demands different QoS. In this paper, we have proposed QoS Guided Weighted Mean Time Min-Min Max-Min Selective heuristic for QoS based task scheduling. The heuristic takes single QoS parameter as requirements of tasks for deciding the match between resources and tasks. The heuristic also considers the performance of resources for scheduling. We have evaluated the heuristic in GridSim, for different task scenarios. The results are obtained and compared with other heuristics like Min-Min, Max-Min, QoS Guided Min-Min, Weighted Mean Time Min-Min Max-Min Selective. The results of the proposed heuristic are better for makespan, resource utilization and resource load balancing than other above mentioned heuristics.