Abstract: Reduction in makespan is a fundamental objective of optimizing task scheduling problems in distributed heterogeneous computing systems. In this study, we propose a new task scheduling heuristic for independent task scheduling in Grid named as QoS Sufferage. Our novel heuristic is based on Sufferage heuristic adapted to include network bandwidth as Quality of Service (QoS) parameter. Numerical simulations are carried out to test our proposed QoS Sufferage heuristic in Grid environment and the results reveal that the proposed QoS Sufferage outperforms other heuristics by achieving a significant reduction in makespan.