Although lots of many-objective evolutionary algorithms have been proposed, most of them cannot effectively deal with many-objective optimization problems with irregular Pareto fronts. In view of the issue, this paper proposes a many-objective evolutionary algorithm based on objective transferring and conditional replacement(MaOEA-OTCR). In the procedure of environmental selection, this algorithm utilizes the designed objective transferring strategy and the developed conditional replacement criterion to select individuals with good convergence and diversity one by one. Specifically, the former first selects these individual located at the boundary of Pareto fronts for determining the boundary of Pareto fronts, while picking out several individuals with better convergence for accelerating the population convergence. Then, it transfers these individuals entered the next generation, and uses the maximum distance between transferred individuals and not transferred individuals to select individuals for the next generation. The latter utilizes the developed conditional replacement criterion based angle and convergence measure to avoid that the former overemphasizes the population diversity. In addition, we propose a multi-criteria decision based mating selection mechanism, which aims at increasing the probability of individuals with favourable convergence and diversity combination, and further promotes the search efficiency of the MaOEA-OTCR. To verify the effectiveness of the MaOEA-OTCR, the MaOEA-OTCR is compared with eight state-of-the-art MaOEAs on three test suites. Experimental results demonstrate that the MaOEA-OTCR not only obtains the highly competitive performance in dealing with many-objective optimization problems, but also has ability to solve many-objective optimization problems with irregular Pareto fronts.