The problem of reachable set estimation and state-feedback controller design for discrete-time systems with time-varying delay under bounded peak disturbances was concerned. Firstly, by choosing appropriate Lyapunov-Krasovkii functional and based on the linear matrix inequality, a sufficient condition was obtained to bound the reachable set of closed-loop systems, that was, a delay-dependent result containing one nonconvex scalar. When the initial value of the system was not zero, these conditions guaranteed the existence of the ellipsoid containing the system state. Secondly, in the process of reachable set estimation, a state-feedback controller was designed to determine ellipsoid which contained the reachable set of the closed-loop system. Thirdly, in order to make the estimated ellipsoid as small as possible, the minimum ellipsoid problem was transformed into an optimization problem with matrix inequality constraints. Finally, numerical examples were given to verify the effectiveness of the obtained results.