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In this article, the non-fragile finite-time H ∞ state estimation problem of neural networks is discussed with distributed time-delays. Based on a modified Lyapunov–Krasovskii functional and the linear matrix inequality (LMI) technique, a novel delay-dependent criterion is presented such that the error system is finite-time boundedness with guaranteed H ∞ performance. In order to obtain less conservative results, Wirtingers integral inequality and reciprocally convex approach are employed. The estimator gain matrix can be achieved by solving the LMIs. Finally, Numerical examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]