Abstract: One of the most important problems in grid computing is task scheduling between resources.This paper presents a scheduling algorithm based on quantum genetic algorithm，whose primary aim is to get the shortest makespan，and the secondary aim to improve the resources use factor.Indirect quantum bit coding method is adopted in this algorithm.It uses the DAG to define the relationship between subtasks，and ranks the subtasks according to the depth-value.Simulation demonstrates that the shortest makespan and resources use factor of this algorithm are better than those of scheduling algorithm based on simple genetic algorithm.