Two kinds of modified particle swarm optimization(PSO) algorithms called particle swarm optimization with ring-star topology and particle mutation(RSMPSO) and particle swarm optimization with ring-von neumann topology and particle mutation(RVMPSO) are presented based on topology and mutation of particle swarm, which enable the diversity and convergence of the particle swarm to be preserved in optimizing procedure to improve the optimization performance of the PSO algorithm. In the modified PSO algorithms, the ring topology with information directionally flowing is combined with star topology or square topology. This strategy enables the particle to have more diversity during the early-stage optimizing to guarantee the search extent. And in the later period, this strategy enables the particle swarm to be converged to make sure the accuracy of optimizing. Meanwhile, a mutation strategy with random walk in a biased way in cuckoo search(CS) algorithm is introduced to the modified PSO algorithm to improve the ability of particle of escaping the local optimum. The simulation experiment on the standard test function shows that, compared with other six algorithms, the modified PSO algorithm possesses the features of easy operation and high optimizing accuracy, and a better performance in diversity and robustness.