In a practical computational grid system, task scheduling in local resource management normally is affected by the arrival rate of tasks and the sizes of tasks, that is, the scheduler must deal with the dynamic task flow. On the long-term viewpoint it is necessary and possible to improve the performance of the scheduler serving the dynamic task flow. In this paper we developed a scheduling strategy which adapts to the dynamic task flow and a genetic algorithm which balances the loads of the nodes furthest. We simulated task flows with several arrival rates and average sizes of tasks, the scheduler with our strategy and algorithm, and the schedulers with other strategies and algorithms. The simulation results show that our scheduler can adapt to the change of arrival rates better than other schedulers.