This paper presents a new genetic algorithm approach to multiobjective optimization problems--incremental multiple objective genetic algorithms (IMOGA). Different from conventional MOGA methods, it takes each objective into consideration incrementally. The whole evolution is divided into as many phases as the number of objectives, and one more objective is considered in each phase. Each phase is composed of two stages. First, an independent population is evolved to optimize one specific objective. Second, the better-performing individuals from the single-objecive population evolved in the above stage and the multiobjective population evolved in the last phase are joined together by the operation of integration. The resulting population then becomes an initial multiobjective population, to which a multiobjective evolution based on the incremented objective set is applied. The experiment results show that, in most problems, the performance of IMOGA is better than that of three other MOGAs, NSGA-II, SPEA, and PAES. IMOGA can find more solutions during the same time span, and the quality of solutions is better.