The simple multi-period repetitive control system proposed by Yamada and Takenaga is a type of servomechanism for the periodic reference input. That is, the simple multi-period repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. In addition, simple multi-period repetitive control systems make transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada and Takenaga clarified the parameterization of all stabilizing simple multi-period repetitive controllers. Recently, the parameterization of all robust stabilizing simple multi-period repetitive controllers for time-delay plants with uncertainty was clarified by Yamada et al. However, using the method by Yamada et al., it is complex to specify the low-pass filters in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. The purpose of this paper is to propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for time-delay plants with the specified input-output characteristic such that the input-output characteristic can be specified beforehand.