In this paper, we present a neural network identification and a control of highly complicated nonlinear left ventricular assist device(LVAD) system with a pneumatically driven mock circulation system. Generally, the LVAD system needs to compensate for nonlinearities. It is necessary to apply high performance control techniques. 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 identification(NNI). Once the NNI has learned the dynamic model of the LVAD system, the other network, called neural network controller(NNC), is designed for a control of the LVAD system. The ability and effectiveness of identifying and controlling the LVAD system using the proposed algorithm will be demonstrated by computer simulation.