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The goal of grid computing is to provide powerful computing abilities for those complicated tasks by using all available and free computational resources. So efficient task scheduling is critical to achieve high performance. In this paper according to the dynamics of the grid, especially to the dynamic QoS requests of the users, we describe multiple QoS attributes as utility functions. Meanwhile, considering that to balance resource loads and minimize makespan are two vital system goals in grid scheduling, we introduce the notion of system utility, define the load balance degree to guide and evaluate the scheduling. Based on these a heuristic scheduling algorithm called user QoS and system index guided task scheduling algorithm (UQSI) is presented to schedule independent tasks with multiple QoS requirements. Simulation results reveal that it can satisfy the users' demands well and improve the system's performance. It is more suitable for the complex grid environment.