The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach.