The robust controller for the nuclear reactor power control system is designed. The nuclear reactor is modeled by use of the point kinetics equations and the singly lumped energy balance equations, Since the model is not exact, the controller which can make the actual system robust is necessary. The perturbed plant is investigated by employing the uncertainties of the initial power level and the physical properties, and by introducing the delay into the modeled plant The overall system is configured into the two port model and the H$infty$ controller is designed. In designing the H$infty$ controller, two factors of the loop shaping and the permissible magnitude of control input are taken into account The designed controller provides the sufficient margins for the robustness, and the transients of the system output power and the control input satisfy their associated requirement.