In this paper, robust fuzzy neural networks (FNNs) are proposed to identify chaotic systems. In the proposed FNNs, integrating support vector regression (SVR) and annealing robust time-varying learning algorithm (ARTVLA) is adopted to optimize the structure of neural networks. In the evolutionary procedure, first, SVR is adopted to determine the number of hidden layer nodes and the initial structure of the FNNs. After initialization, ARTVLA with nonlinear time-varying learning rate is then applied to train FNNs. In ARTVLA, a computationally efficient optimization method, particle swarm optimization (PSO), is adopted to simultaneously find optimal learning rates. With the promising learning rates, the ARTVLA- based FNNs (ARTVLA-FNNs) can overcome the stagnation in searching promising solutions. Due to the advantages of SVR and ARTVLA-FNNs (SVR-ARTVLA-FNNs), the proposed SVR-ARTVLA-FNNs have good performance for identifying chaotic systems. Simulation results are illustrated the feasibility and superiority of the proposed SVRARTVLA-FNNs.