The performance and stability of Adaptive Neuro-Fuzzy Inference System (ANFIS) depend on its network structure and preset parameter selection, and Particle Swarm Optimization-ANFIS (PSO-ANFIS) easily falls into the local optimum and is imprecise. A novel ANFIS algorithm tuned by Chaotic Particle Swarm Optimization (CPSO-ANFIS) is proposed to solve these problems. A chaotic ergodic algorithm is first used to improve the PSO and obtain a CPSO algorithm, and then the CPSO is used to optimize the parameters of ANFIS to avoid falling into the local optimum and improve the performance of ANFIS. Based on the deformation data from the Xiaolangdi Dam in China, three neural network algorithms, ANFIS, PSO-ANFIS, and CPSO-ANFIS, are used to establish the dam deformation prediction models after data preparation and selection of influencing factors for the dam deformation. The results are compared using evaluation indicators that show that CPSO-ANFIS is more accurate and stable than ANFIS and PSO-ANFIS both in predictive ability and in predicted results.