In this paper, we present neural network for control of Left Ventricular Assist Device(LVAD) system with a pneumatically driven mock circulation system. Beat rate(BR), Systole-Diastole Rate(SDR) and flow rate are collected as the main variables of the LVAD system. System modeling is completed using the neural network with input variables(BR, SBR, their derivatives, actual flow) and output variable(actual flow). It is necessary to apply high perfomance control techniques, since the LVAD system represent nonlinear and time-varing characteristics. Fortunately. the neural network can be applied to control of a nonlinear dynamic system by learning capability In this study, we identify the LVAD system with neural network and control the LVAD system by PID controller and neural network feedforward controller. The ability and effectiveness of controlling the LVAD system using the proposed algorithm will be demonstrated by experiment.