This paper proposes a problem-solving method for the stroke limitation problem, which is related to auxiliary masses of active mass damper systems for high-rise buildings. The proposed method is used in a new simple control system for the active mass dampers mimicking the motion of bipedal mammals, which has a neural oscillator synchronizing with the acceleration response of structures and a position controller. In the system, the travel distance and direction of the auxiliary mass of the active mass damper is determined by reference to the output of the neural oscillator, and then, the auxiliary mass is transferred to the decided location by using a PID controller. The one of the purpose of the previouslyproposed system is stroke restriction problem avoidance of the auxiliary mass during large earthquakes by the determination of the desired value within the stroke limitation of the auxiliary mass. However, only applying the limited desired value could not rigorously restrict the auxiliary mass within the limitation, because the excessive inertia force except for the control force produced by the position controller affected on the motion of the auxiliary mass. In order to eliminate the effect on the auxiliary mass by the structural absolute acceleration, a cancellation method is introduced by adding a term to the control force of the position controller. We first develop the previously-proposed system for the active mass damper and the additional term for cancellation, and verity through numerical experiments that the new system is able to operate the auxiliary mass within the restriction during large earthquakes. Based on the comparison of the proposed system with the LQ system, a conclusion was drawn regarding which the proposed neuronal system with the additional term appears to be able to limit the stroke of the auxiliary mass of the AMD.