An accelerate convergence particle swarm optimization(ACPSO) algorithm is proposed based on analyzing the convergence of basal particle swarm optimization(BPSO) algorithm. The convergence speed of ACPSO algorithm is very quickly through theoretical analysis. Then the parameters in this algorithm are optimized. The mutation operator of depending on segmental worst particles’ information is shown to escape the local optimal. The performance of ACPSO algorithm with the optimal parameters is tested on several classical functions by comparing with four classical PSO algorithms. The experimental results show that the ACPSO algorithm is efficient and robust. Especially, the convergence speed of ACPSO is superior to several classical PSO algorithms obviously.