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In this paper, the global asymptotic stability problem of Takagi-Sugeno (TS) fuzzy Cohen-Grossberg Bidirectional Associative Memory neural networks (FCGBAMNNs) with discrete and distributed time-varying delays is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of FCGBAMNNs which are represented by TS fuzzy models. Our results can be easily verified and are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks and cellular neural networks. Finally, the proposed stability conditions are demonstrated with a numerical example.