This paper presents a new Multi-Objective Particle Swarm Optimization (MOPSO) algorithm that has two new components: leader selection and crossover. The new leader selection algorithm, called Space Expanding Strategy (SES), guides particles moving to the boundaries of the objective space in each generation so that the objective space can be expanded rapidly. Besides, crossover is adopted instead of mutation to enhance the convergence and maintain the stability of the generated solutions (exploitation). The performance of the proposed MOPSO algorithm was compared with three popular multi-objective algorithms in solving fifteen standard test functions. Their performance measures were hypervolume, spread and inverse generational distance. The performance investigation found that the performance of the proposed algorithm was generally better than the other three, and the performance of the proposed crossover was generally better than three popular mutation operators.