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This paper addresses the event-triggered H∞ state estimation problem for a class of discrete recurrent neural networks subject to variance-constraint and fading measurements. The phenomena of fading measurements are described by introducing a set of mutually independent random variables, which reflect that each sensor has individual missing probability. In addition, for the purpose of energy saving, an event-triggered H∞ state estimation scheme is used for time-varying neural networks to determine whether the measurement output is transmitted to the estimator or not. Some sufficient conditions are obtained to guarantee that the estimation error system satisfies both estimation error variance constraint and prescribed H∞ performance requirement. Finally, the feasibility of the proposed event-triggered H∞ state estimation method is verified by a numerical example.