In this paper, we study disturbance-attenuation characteristic of a structure of time-delay system with communication disturbance observer (CDOB). A time-delay compensation method based on network disturbance (ND) concept and CDOB has been proposed and used in various kinds of time-delay systems and the effectiveness has been verified theoretically and experimentally. The advantage is that it works even when a time-delay value is unknown or a time-delay model is unavailable, since it does not need a time-delay model. However, it has been pointed out that the system-model error seriously affects the steady-state characteristics and causes steady-state error. Then, some approaches to handle such a problem have been proposed so far. It has turned out that one of those proposed approaches overcomes such a problem and achieves zero steady-state error in case that there are system-model errors. However, the robustness against disturbance, or the disturbance-attenuation characteristic has not been studied. Therefore, in this paper, the disturbance-attenuation characteristic of the structure is studied. The characteristic is studied compared with that of the conventional structure.