In this paper, we present a dynamic output-feedback receding horizon $H_{infty}$controller for linear discrete-time systems with disturbance. The controller is obtained numerically from the finite horizon output-feedback $H_{infty}$optimization problem, which is, in fact, hardly solved analytically. Under a matrix inequality condition on the terminal weighting matrix, the monotonic decreasing property of the cost is shown. This property guarantees both the closed-loop stability and the $H_{infty}$norm bound. Then, we extend the proposed design method to a reference tracking problem and a problem for time-varying systems. Numerical examples are given to illustrate the performance of the proposed controller.