This paper addresses the problem of exponential stabilization of a class of time-varying delay systems with nonlinear perturbations. These perturbations are related not only with current state xt and the delayed state xt−ht but also with βt, where βt is a continuous function defined on [0,+∞). With the delay interval divided into two equidistant subintervals, a novel Lyapunov functional is introduced, and several new exponential stabilization criteria are derived in terms of linear matrix inequalities (LMIs) by employing reciprocally convex approach. Two examples are given to illustrate the effectiveness of the main results.