In this paper, we present the PID control method for the controlling flow rate of highly complicated nonlinear Left Ventricular Assist Device(LVAD) with pneumatically driven mock circulatory system. Beat Rate (BR), Systole-Diastole Rate (SDR) and flow rate are used as the main variables of the LVAD system. System modeling is completed using the neural network with input variables (BR, SDR, their derivatives, actual flow) and an output valiable(actual flow). Then, as the basis of this model, we perform the simulation of PID control to predict the performance and tendency of the system and control the flow rate of LVAD system using the PID controller. The ability and effectiveness of identifying and controlling a LVAD system using the proposed algorithm will be demonstrated through computer simulation and experiments.