Abstract: The state estimation problem was studied for neural networks with mixed discrete and distributed time-varying delays as well as general activation functions. The discrete time-varying delay varies in an interval, where the lower bound is not fixed to be zero. Defining a novel Lyapunov functional and using the Jensen integral inequality, a delay-interval-dependent criterion is provided to design a state estimator through available output measurements in terms of a linear matrix inequality (LMI), such that the error-state system is globally asymptotically stable. A numerical example was given to illustrate that this result is more effective and less conservative than some existing ones.