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In this paper, dynamic behavior of a class of high-order fuzzy cellular neural networks (HFCNNs) with time-varying delays is investigated. Compared with the previous results in the literature, the restrictions are loosed, since we do not assume the boundedness and monotonicity on the activation functions, and the differentiability of time-varying delay functions. Some sufficient conditions are derived for ascertaining the existence, uniqueness and exponential stability of equilibrium point and uniform boundedness of solutions of the HFCNNs. Finally, two examples are given to show the effectiveness of the proposed criteria, which complement some previously known results.