A multi-objective particle swarm optimization algorithm based on the random black hole particle swarm optimization(RBH-PSO) and step-by-step elimination strategy is proposed. The Pareto optimal solutions are approached by its advantage of speeding up the convergence and improving the performance of global optimizer greatly. To avoid the disadvantage of crowding distance sorting technique, the step-by-step elimination(SE) strategy is proposed, which is used to select the particles from one iteration to another. In addition, dynamic selection of leader particle for each particle, adaptive inertia weight and a special mutation operation are incorporated to enhance the global exploratory capability and avoid premature convergence. The performance of the proposed algorithm is tested on a set of well-known benchmark functions and compared with several representative multi-objective optimization algorithms. Simulation results show that the MRBHPSO-SE algorithm can converge to the global optimal with high accuracy while keeping the good diversity of the Pareto solutions.