This paper deals with the problem of the robust passivity for genetic regulatory networks with interval time-varying delays and norm-bounded parameter uncertainty. The regulatory functions are assumed to satisfy the globally Lipschitz continuous conditions. The interval time-varying delays exist in both the translation process and the feedback regulation process. Based on an improved bounding technique, a delay-dependent robust passivity condition is derived in terms of linear matrix inequalities (LMIs). The delay-dependent criterion is dependent on the lower and upper bounds of the time-varying delays. By an improved bounding technique, free-weighting matrices are introduced to reduce the conservatism of the criterion. The important feature of the results is to improve upper bounds to introduce some degree of conservativeness. The numerical example demonstrates the effectiveness and applicability of the proposed results.