A particle swarm algorithm with two types of normal mutations is proposed for the multi-objective problem. One of variations contributes to discover new Pareto optimal solutions in the neighborhoods of these existing solutions, the other can disperse the swarm. The searching process is divided into three stages, and those particles which guide the others are selected with different targeted strategies in each stage. Numerical results show that the algorithm can significantly improve the diversity and convergence of the Pareto optimal solution.