Aiming at the characteristics that many cluster intelligent algorithms are easy to fall into local optimum and have slow convergence rate, a new algorithm (PK algorithm) with less parameter settings and strong global search ability is proposed. The comparison of 10 benchmark functions with particle swarm optimization algorithm verifies the effectiveness of the algorithm, because the average and minimum values of the PK algorithm under 30 trials are better than the particle swarm optimization algorithm. Then using the PK algorithm to optimize the BP neural network, and 11 test data sets were classified. The experimental results show that the BP neural network based on PK algorithm has better performance than the original algorithm on 11 test sets, and the performance is superior to BP neural network based on genetic algorithm on most test sets. Thus, we conclude that the BP neural network based on PK algorithm can effectively improve the classification accuracy and enhance the robustness.