The integral inequality technique is widely used to derive delay-dependent conditions, and various integral inequalities have been developed to reduce the conservatism of the conditions derived. In this study, a new integral inequality was devised that is tighter than existing ones. It was used to investigate the stability of linear systems with a discrete distributed delay, and a new stability condition was established. The results can be applied to systems with a delay belonging to an interval, which may be unstable when the delay is small or nonexistent. Three numerical examples demonstrate the effectiveness and the smaller conservatism of the method. (C) 2015 Elsevier Ltd. All rights reserved.