This paper presents a Neural Network Identification(NNI) method for modeling of highly complicated nonlinear and time varing human system with a pneumatically driven mock circulatory system of Left Ventricular Assist Device(LVAD). This system consists of electronic circuits and pneumatic driving circuits. The initiation of systole and the pumping duration can be determined by the computer program. The line pressure from a pressure transducer inserted in the pneumatic line was recorded System modeling is completed using the adaptively trained backpropagation learning algorithms with input variables, heart rate(HR), systole-diastole rate(SDR), which can vary state of system. Output parameters are preload, afterload which indicate the systemic dynamic characteristics. Consequently, the neural network shows good approximation of nonlinearity, and characteristics of left Ventricular Assist Device. Our results show that the neural network leads to a significant improvement in the modeling of highly nonlinear Left Ventricular Assist Device.