In this paper, we examine the parameterization of all stabilizing multi-period repetitive controllers for single-input/single-output time-delay plants with the specified input-output characteristic. The parameterization is the problem to find all stabilizing controllers. The parameterization of all stabilizing multi-period repetitive controllers for non-minimum-phase plants and that of all stabilizing multi-period repetitive controllers for time-delay plants were solved by Yamada and Satoh. However, using the method by Yamada and Satoh, we cannot settle input-output characteristics easily. Because the input-output characteristic is related to four free parameters. If the parameterization of all stabilizing multi-period repetitive controllers with the specified input-output characteristic, which is the parameterization when low-pass filters are settled beforehand, is obtained, we can specify the input-output characteristic easily. In this paper, we propose the parameterization of all stabilizing multi-period repetitive controllers for time-delay plants with the specified input-output characteristic.