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The particle swarm optimization (PSO) is an algorithm to find out optimal solution in search space by interactions of individuals among particle population. Even though the hierarchical PSO (HPSO) algorithm, which is consisted of fast position convergence particle swarm optimization (fPSO) layer and mutation layer, has been shown to perform well,but the analysis of convergent condition of fPSO hasn't been given by the authors. In this paper, the convergent sufficient condition of fPSO in is derived mathematically, and a HPSO like mutated fPSO (mfPSO) is constructed too. Results of experiments show that the introduced mfPSO performed superiority to HPSO on benchmarks.