This paper is concerned with the problem of Robust H∞ controller design for a class of uncertain networked control systems (NCSs). The network-induced delay is of an interval-like time- varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be norm-bounded and possibly time-varying. Based on Lyapunov-Krasovskii functional approach, a robust H∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay-dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H∞ performance level of the closed-loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.