Recently, it was found that most multiobjective particle swarm optimizers (MOPSOs) perform poorly when tackling many-objective optimization problems (MaOPs). This is mainly because the loss of selection pressure that occurs when updating the swarm. The number of nondominated individuals is substantially increased and the diversity maintenance mechanisms in MOPSOs always guide the particles to explore sparse regions of the search space. This behavior results in the final solutions being distributed loosely in objective space, but far away from the true Pareto-optimal front. To avoid the above scenario, this paper presents a balanceable fitness estimation method and a novel velocity update equation, to compose a novel MOPSO (NMPSO), which is shown to be more effective to tackle MaOPs. Moreover, an evolutionary search is further run on the external archive in order to provide another search pattern for evolution. The DTLZ and WFG test suites with 4-10 objectives are used to assess the performance of NMPSO. Our experiments indicate that NMPSO has superior performance over four current MOPSOs, and over four competitive multiobjective evolutionary algorithms (SPEA2-SDE, NSGA-III, MOEA/DD, and SRA), when solving most of the test problems adopted.