In this note, the problem of state bounding for linear time-varying systems with delay and bounded disturbances input is considered for the first time. By using a novel approach which does not involve the Lyapunov-Krasovskii functional method, new explicit delay-independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it. A numerical example is given to illustrate the effectiveness of the obtained result. (C) 2014 Elsevier Ltd. All rights reserved.