The particle swarm optimization algorithm is an effective tool to solve various optimization problems due to the small number of parameters and the simple learning strategy. However, the updated strategy from the basic PSO mainly aims to learn the global optimal particles, and it often leads to premature convergence with poor solution accuracy. An adaptive complex network topology with a fitness distance correlation for the particle swarm optimization algorithm is proposed (CNAPSO). Using the CNAPSO algorithm, it is concluded that different network topologies have different degrees of dispersion in the process of particle swarm optimization search. Therefore, the adaptive strategy with the fitness distance correlation proposes to effectively balance the global exploration and local exploitation capabilities, which is the particle swarm adaptive network neighborhood topology. The neighborhood topology construction strategy with a complex network is used to construct the neighborhood topology for each particle. Therefore, the local optimal particles in the neighborhood participate in the search process of particle swarm optimization and eliminate the situation of only learning the global optimal particles. Moreover, it improves the solution accuracy of the particle swarm optimization algorithm. In addition, to avoid the particle swarm falling into premature convergence, this study introduces a random drift strategy to make the particles drift slightly and reduces the risk of premature convergence. The experimental results on twenty-four benchmark functions show that CNAPSO has great improvements in the accuracy of the solution and the speed of convergence compared with the six representative PSO algorithms.