A stable control system is easily designed with the simple adaptive control (SAC) method by using the almost strictly positive real (ASPR) condition of a plant. For the plant that does not satisfy ASPR, an SAC system can be designed by adding a parallel feed-forward compensator (PFC) to the plant. However, in this case, steady-state error between the plant output and the reference model output may remain because of the PFC output. To solve this problem, the null-space adjustor which cancels the PFC input on the steady-state of the system, has been proposed. In our study, an SAC system with the null-space adjustor was extended using a disturbance compensator. We showed the boundedness of the signal in the proposed SAC system and confirmed the effectiveness of the proposed method by the numerical simulation.