In the next generation of baby carriages, better comfort for both the baby as well as the parent is required, in addition to safety concerns. To develop a comfortable baby carriage, fundamental data are required about the types of vibrations babies prefer and find pleasant. In order to obtain such data, it is necessary to develop a shaking table for baby carriages having nonlinear characteristics, and develop a control system in which the shaking table follows a desired input characterized as a random wave. In this study, a single axis shaking table for a baby carriage is studied. The table under the right front wheel of the baby carriage is shaken according to a desired waveform. The proposed control system is a proportional controller with an outer feedback loop based on a discrete-time sliding mode controller, i.e., an input waveform shaping filter. The performance of the controller is evaluated using a numerical simulation. The results show that although the shaking table displacement could follow the desired waveform by using only the proportional controller, the robustness of the response to disturbance was weak, and also that the robustness could be improved with the addition of the proposed input waveform shaping filter. The effectiveness is demonstrated using a control experiment. The results of this experiment show that the mean square error of the table displacement when using proportional controller along with the input waveform shaping filter was about 75% compared with the error when using only the proportional control.