In various conditions of blood demand of circulatory system, the autonomic regulations system of body regulates the heart rate (HR) to maintain the arterial pressure (AP) constant, where the HR is considered as the controlled variable indicating the blood demands of the circulatory system. Therefore, model-free adaptive controller is used to regulate the pump speed based on the HR. As a key feature, the proposed controller provides a defined and adjustable HR and automatically regulates the pump speed according to the status of circulatory system. A mathematic model of the cardiovascular- baroreflex system is used to describe this mechanism and to test the controller in the presence of failing left ventricle and slightly physical active. The simulation results demonstrate that the HR is kept stable. Furthermore, no matter the peripheral resistance disturbance or the change of the desired HR, the settling time of the controller is <5 seconds without overshoot or static error.