The R2 indicator and decomposition based multiple particle swarm optimizer(R2-MOPSO) is suitable for solving two and three objectives optimization problems in terms of the convergence and diversity. However, it is difficult for the R2-MOPSO to address many-objective optimization problems(MaOPs). Therefore, we propose an R2 indicator and objective space partition based many-objective particle swarm optimizer(R2-MOPSO-II) to solve MaOPs. Firstly, a new bi-level archive maintainence strategy is introduced to balance the convergence and diversity after considering the R2 indicator and the objective space partition strategy. Then, a new leader selection strategy gives the bridge between objective space and decision variable space. The modified velocity updated equation based on bi-level archive is introduced to balance the exploration and exploitation. Finally, the Gaussian learning strategy and the elitist learning strategy are embedded into the proposed algorithm to help the algorithm jump out of local Pareto front. The numerical simulation results show that the proposed algorithm has achieved better convergence and diversity for solving DTLZ and WFG test instances.