In order to balance the local exploitation ability and the global exploration ability of artificial bee colony,and accelerate the rate of convergence, a multi-objective artificial bee colony based on the limit search(LSABC) strategy is proposed. Firstly, a chaotic mirroring strategy is proposed in the initialization phase to ensure diversity and superiority. Then, the radius of search is dynamically adjusted while the employed bees and the onlooker bees searching according to the individual limit, which improves the search accuracy and convergence speed. The development times of the external archive are combined to choose elite solution so as to guide evolution reasonably. Finally, experiments are conducted on a set of 11 benchmark functions, and the results show that the proposed algorithm performs well in convergence and distribution.