In recent decades, to efficiently solve multi-objective optimization problems, researchers have further studied and proposed many improved multi-objective particle swarm optimization algorithms, most of which adopt fixed population size. In the search process, if the population size is not set properly, it will affect the search effect of the algorithm and the calculation time will be too long. Meanwhile, these algorithms still have some challenges in balancing diversity and convergence. To deal with the above problems, a multi-objective particle swarm optimization based on maintaining dynamic population size (MOPSO-MDP) is proposed. Firstly, an improved update strategy of personal best solution and global best solution is introduced into the algorithm, which is helpful to improve its search ability and its ability to jump out of the local optimum. Then, the algorithm introduces a strategy of maintaining population growth, which can improve the quality of individuals and the diversity of the population. At the same time, a maintaining population reduction strategy is also proposed, which helps to maintain the quality of individuals in the population and avoid too long calculation time of the algorithm. Finally, the numerical experiments compare the proposed MOPSO-MDP with ten typical evolutionary algorithms on selected 22 test problems. The numerical experimental results show that the proposed MOPSO-MDP has noticeable advantages in population diversity and convergence ability on these 22 test problems.