A hybrid learning neuro-fuzzy system with asymmetric fuzzy sets (HLNFS-A) is proposed in this paper. The learning methods of random optimization (RO) and least square estimation (LSE) are used in hybrid way to train the system parameters of HLNFS-A to achieve stable and fast convergence. In the HLNFSA, the premise and the consequent parameters are updated by RO and LSE, respectively. With the proposed asymmetric fuzzy sets (AFS), the neuro-fuzzy system can capture the essence of nonlinear property of dynamic system, when used in the application of modeling. To demonstrate the feasibility and the potential of the proposed approach, an example of chaotic time series for system identification and prediction is given to verify the nonlinear mapping capability of the HLNFS-A. The experimental results show that the proposed HLNFS-A can achieve excellent performance for system modeling.