This paper develops a decomposition-based coevolutionary algorithm for many-objective optimization, which evolves a number of subpopulations in parallel for approaching the set of Pareto optimal solutions. The many-objective problem is decomposed into a number of subproblems using a set of well-distributed weight vectors. Accordingly, each subpopulation of the algorithm is associated with a weight vector and is responsible for solving the corresponding subproblem. The exploration ability of the algorithm is improved by using a mating pool that collects elite individuals from the cooperative subpopulations for breeding the offspring. In the subsequent environmental selection, the top-ranked individuals in each subpopulation, which are appraised by aggregation functions, survive for the next iteration. Two new aggregation functions with distinct characteristics are designed in this paper to enhance the population diversity and accelerate the convergence speed. The proposed algorithm is compared with several state-of-the-art many-objective evolutionary algorithms on a large number of benchmark instances, as well as on a real-world design problem. Experimental results show that the proposed algorithm is very competitive.