In this brief, a nonlinear model-based feedback linearization (FBL) control is proposed for a high-performance cardiovascular circulatory simulator (CCS). The challenges are that the piston pump used for a mock ventricle in CCS has high-bandwidth pressure dynamics and hard nonlinearity due to check valves. Limited control performance in the previous researches due to these difficulties even raises the question of the physiological feasibility of the developed CCS. To overcome this problem, FBL theory based on the Lie algebra is applied in this research for the piston pump mock ventricle control. Dynamic model of the piston pump was derived, and parameter values of the model were identified experimentally for the controller design. The experimental results confirmed good performance of the proposed controller for various physiological scenarios. Good match with the reference model behavior was verified as well, and physiological feasibility of the CCS was secured thereby thanks to the proposed high-performance controller.