The application of multiobjective evolutionary algorithms to many-objective optimization problems often faces challenges in terms of diversity and convergence. On the one hand, with a limited population size, it is difficult for an algorithm to cover different parts of the whole Pareto front (PF) in a large objective space. The algorithm tends to concentrate only on limited areas. On the other hand, as the number of objectives increases, solutions easily have poor values on some objectives, which can be regarded as poor bottleneck objectives that restrict solutions' convergence to the PF. Thus, we propose a coevolutionary particle swarm optimization with a bottleneck objective learning (BOL) strategy for many-objective optimization. In the proposed algorithm, multiple swarms coevolve in distributed fashion to maintain diversity for approximating different parts of the whole PF, and a novel BOL strategy is developed to improve convergence on all objectives. In addition, we develop a solution reproduction procedure with both an elitist learning strategy (ELS) and a juncture learning strategy (JLS) to improve the quality of archived solutions. The ELS helps the algorithm to jump out of local PFs, and the JLS helps to reach out to the missing areas of the PF that are easily missed by the swarms. The performance of the proposed algorithm is evaluated using two widely used test suites with different numbers of objectives. Experimental results show that the proposed algorithm compares favorably with six other state-of-the-art algorithms on many-objective optimization.