The scheduling problem that maps independent tasks to heterogeneous resources in distributed computing systems is known as NP-complete［1］. GRID［2］ is an example of distributed systems that consisted of heterogeneous resources. Many algorithms to solve this problem have been presented［1,3,4,5］. The scheduling algorithm can be classified into static scheduling algorithms and dynmic scheduling algorithms. A dynamic scheduling algorithm can be used when we can not predict the priority of tasks. Moreover, a dynamic scheduling algorithm can be divided into on-line mode algorithm and batch mode algorithm according to the scheduling time［1,6］. In this paper, we propose a new on-line mode scheduling algorithm. By extensive simulation, we can see that our scheduling algorithm outperforms previous scheduling algorithms.