Artificial bee colony (ABC) is a well-known swarm intelligence algorithm that has been widely applied to many optimization problems. However, ABC shows some shortcomings in tackling many-objective optimization problems (MaOPs). In this paper, a novel many-objective ABC based on dual indictors (called DIMABC) is proposed to solve MaOPs. In DIMABC, a convergence indicator based on favorable weights is used to guide the search, mating selection and environmental selection. Based on the convergence indicator, good solutions are selected to construct an elite set, which is used to construct a new search strategy. In addition, the probability selection model is also improved based on the convergence indicator in the onlooker bee stage. Finally, a new diversity indicator and the convergence indicator are used in the environmental selection to make a balance between convergence and diversity. To validate the optimization capability of the proposed DIMABC, nine WFG benchmark problems with 3, 5, 8, and 15 objectives are utilized. Experimental results show that DIMABC obtains superior performance when compared with five other well-established algorithms.