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Optimization problems with multiple objectives are often encountered in many scientific and engineering scenarios. The prior works on multi-objective differential evolution (DE) have mainly focused on nondominated sorting of solutions to handle different objectives at the same time. This paper suggests a new approach to differential evolution which is based on decomposition of the original problem into a set of scalar optimization subproblems. We design a decomposition-based DE algorithm to optimize these scalar subproblems simultaneously by evolving a population of solutions with proper mutation and selection operators. Since the proposed DE algorithm does not involve pairwise comparison and non-dominated sorting of solutions, it would incur lower computational complexity than the dominance-based DE algorithms.