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Task scheduling and quality of service (QoS) are two curial problems in grid computing. Focusing on the meta-task with QoS requirements, this work presents an ant colony optimization for grid task scheduling with multiple QoS dimensions (QACO). The proposed algorithm considers five kinds of QoS dimensions: time, reliability, version, security and priority which are transformed to utility as the heuristic information of the algorithm. The objective of the algorithm is maximizing the total utility. Simulation studies compare the performance of QACO, QoS-Min-Min and the improved Min-Min. Simulation results shown that QACO finds the best results.