In this paper, a novel Takagi-Sugeno recurrent fuzzy neural network (TSRFNN) is constructed for modeling and sensor fault diagnosis of a Continuous Stirred Tank Reactor (CSTR), a nonlinear dynamic system. The TSRFNN is composed of 9 layers, including premise network and consequence network. The temporal information is embedded in the TSRFNN by adding the feedback connections between the output layer and the input layer of the fuzzy neural network (FNN). It is assumed that the inputs are Gaussian membership functions; the product operation is utilized for the premise and implication, and the weighted center-average method is adopted for defuzzification. The network is a Fuzzy Basis Function(FBF). The general approximation characteristic of the network was proven by the theory reasoning. The identification of the TSRFNN consists of two steps: structure identification and parameter identification. Unsupervised clustering is used to determine the structure of the fuzzy system, the number of fuzzy rules, and the membership functions of the premise using the input-output data of a system. Then in the parameter identification, the Dynamic Backpropagation (DBP) is adopted to determine the membership functions of the conclusion of the fuzzy system.