A new fuzzy ART neural network model based on closeness theory, called CBFART for short, is introduced in this paper. The new network model is formed by incorporating the two concepts of fuzzy set theory, closeness and closest principles, with adaptive resonance theory (ART). The learning of the model is characterized by matching-consigning cycle, and the classification of patterns in the network conforms to the closest principle. Coding complement, matching-consigning, and fast consigning - slow recoding procedure work together to make sure that learning of the network is converging and stable. The above three elements also make one shot learning practicable, so as to improve the learning speed of the network. The concrete algorithm of the model and the result of simulation are given in the paper, and the analysis shows that the model is good in clustering performance.