In this paper we address the problem of vibration reduction of buildings with delayed measurements, where the delays are time-varying and bounded. We focus on a convex optimization approach to the problem of state-feedback H-infinity control design. An appropriate Lyapunov-Krasovskii functional and some free weighting matrices are used to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities (LMIs). The controller, which guarantees asymptotic stability and an H∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated through the simulation of an n-story base-isolated building