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The robust state estimation problem for a class of uncertain neural networks with time-varying delay is studied in this paper. The parameter uncertainties are assumed to be norm bounded. Based on a new bounding technique, a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks. The criterion is dependent on the size of the time-varying delay and on the size of the time derivative of the time-varying delay. It is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally, two simulation examples are given to demonstrate the effectiveness of the developed approach.