In real-world, there exist lots of many-objective optimization problems (MaOPs), which severely challenge well-known multi-objective evolutioanry algorithms (MOEAs). A many-obective evolutioanry algorithm combining decomposition and coevolution (MaOEA/DCE) is presented in this paper. MaOEA/DCE adopts mix-level orthogonal experimental design to produce a set of weight vectors evenly distributed in weight coefficient space, so as to improve the diversity of initial population. In addition, the MaOEA/DCE integrates differential evolution (DE) with the adaptive SBX operator to generate high-quality offspring for enhancing the convergence of evolutionary population. Some comparative experiments are conducted among MaOEA/DCE and other five representative MOEAs to examine their IGD+ performance on four MaOPs of DTLZ{1,2,4,5}. The experimental results show that the proposed MaOEA/DCE has overall performance advantage over the other peering MOEAs in terms of convergence, diversity, and robustness.