The efforts to construct a national scale grid computing environment has brought unprecedented computing capacity. Exploiting this complex infrastructure requires efficient middleware to support the execution of a distributed application, composed of a set of subtasks, for best performance. This presents the challenge how to schedule these subtasks in shared heterogeneous systems. Current work has several limitations. Most scheduling systems are based on determined estimation of task completion time. Current application-level scheduling algorithms are too closely coupled with application internal structures. The application performance may suffer when some resources represent abnormal usage pattern during applications execution. To address these issues, we develop a prototype of Grid Harvest Service (GHS) to provide dynamic and self-adaptive task scheduling. Experimental results show GHS outperforms current systems in scheduling large applications in a non-dedicated heterogeneous environment.