Particle swarm optimization (PSO) was applied in many fields because of its simplicity and fast convergence, but it is easily prone to be premature and get struck in local optima. Combination with the characteristics of Lévy flight, this paper proposes a new variation of PSO with Lévy mutation (LévyPSO), and then analyzed it's convergence and pointed out that the algorithm convergence in probability for the global optima. The experiments is conducted on 8 classic benchmark functions, the results show that the Lévy mutation can use the current knowledge of particles and increase the diversity of population. Thus, the proposed algorithm has better performance because of it can more effectively balance the global search and local search. The parameters settings of the proposed algorithm are discussed in the final.