Abstract. Deploying lightweight tasks on grid resources would let the communication overhead dominate the overall application processing time. Our aim is to increase the resulting computation-communication ratio by adjusting the task granularity at the grid scheduler. We propose an on-line scheduling algorithm which performs task grouping to support an unlimited number of user tasks, arriving at the scheduler at runtime. The algorithm decides the task granularity based on the dynamic nature of a grid environment: task processing requirements; resource-network utilisation constraints; and users QoS requirements. Simulation results reveal that our algorithm reduces the overall application processing time and communication overhead significantly while satisfying the runtime constraints set by the users and the resources.