It is difficult to solve many-objective optimization problems (MaOPs) effectively by using the traditional multi-objective evolutionary algorithms (MOEAs) based on Pareto dominance relation. A dominance relation is proposed firstly by combing double distances of PBI utility function without introducing extra parameter. Secondly, a diversity maintenance method based on double distances is also defined, which not only considers the double distances of the individual, but also adaptively adjusts the weight of diversity according to the objective number of MaOP, so as to better balance the convergence and diversity of the solution set in many-objective space. Finally, the proposed dominance relation and diversity maintenance method are embedded into the framework of NSGA-II, and then a many-objective evolutionary algorithm based on double distances (MaOEA/d²) is designed. The MaOEA/d² is compared with other five representative many-objective evolutionary algorithms on the DTLZ and WFG benchmark functions with 5-,10-,15-, and 20-objective in terms of IGD and HV indicators. The empirical results show that MaOEA/d²can obtain better convergence and diversity. Therefore, the proposed MaOEA/d²is a promising many-objective evolutionary algorithm.