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The cost of processing and transferring and the time of processing and transferring are critical to the success of a lot of enterprises using cloud computing. Most of the existing optimization algorithms only focus on one aspect. This paper formulates a model for the multi-objective task assignment and describes a particle swarm optimization algorithm in cloud computing environment. The algorithm not only optimizes the time, but also optimizes the cost. The experimental result manifest that the proposed method is more effective and efficient in time and cost.