In this paper, the state estimation problem is investigated for complex-valued neural networks(CVNNS) with discrete interval time-varying delays as well as general activation funcions. By constructing appropriate Lyapunov-Krasovskii functional and employing Newton-Leibniz formulation, linear matrix inequality(LMI) technique and computational criteria in complex domain, some conditions are derived to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. One example are given to show the effectiveness of the theoretical analysis.