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Grid applications in virtue of open service grid architecture (OGSA) are promising next-generation computation techniques. One of the most important and challenging problems about grid application is the workflow scheduling problem to achieve the users' QoS (quality of service) requirements as well as to minimize the cost. This paper proposes an ant colony optimization (ACO) algorithm to tackle this problem. Several new features are introduced to the algorithm. First, we define two kinds of pheromone and three kinds of heuristic information to guide the search direction of ants for this bi-criteria problem. Each ant uses either one from these heuristic types and pheromone types in each iteration based on the probabilities controlled by two parameters. These two parameters are adaptively adjusted in the process of the algorithm. Second, we use the information of partial solutions to modify the bias of ants so that inferior choices will be ignored. Moreover, the experimental results in 3 workflow applications under different deadline constraints show that the performance of our algorithm is very promising, for it outperforms the Deadline-MDP algorithm in most cases.