This paper proposes a recurrent interval type-2 fuzzy neural network with asymmetric membership functions (RT2FNN-A). The RT2FNN-A uses the interval asymmetric type-2 fuzzy sets and it implements the FLS in a five layer neural network structure which contains four layer forward network and a feedback layer. Each asymmetric fuzzy member function (AFMF) is constructed by parts of four Gaussian functions. The corresponding learning algorithm is derived by gradient descent method. Finally, the RT2FNN-A is applied in identification of nonlinear dynamic system. Simulation results are shown to illustrate the effectiveness of the RT2FNN-A systems.