Abstract: A novel Quantum Adaptive Particle Swarm Optimization (QAPSO) method is proposed. In this algorithm, the position encoding of the particle is achieved with quantum bits, and the state of quantum bit is updated dynamically with particle trajectory information. Then the mutation operation is performed by quantum non-gate to avoid falling into local optimum, which increases the diversity of particles. Afterwards, the Radial Basis Function (RBF) neural network is trained with QAPSO to implement the optimization of RBF neural network parameters. The network traffic prediction model is established based on the Quantum Adaptive Particle Swarm Optimization and RBF Neural Network (QAPSO-RBFNN). Forecasting results on real network traffic demonstrate that the convergence speed of the proposed method is faster and prediction accuracy is more accurate than that of traditional RBF neural network, the Particle Swarm Optimization and RBFNN (PSO-RBFNN), Hybrid Particle Swarm Optimization and RBFNN (HPSO-RBFNN), Adaptive Particle Swarm Optimization and RBF Neural Network (APSO-RBFNN). Furthermore, the forecasting effect of this method is stable on different scales.