In this paper, a self-driving vehicle longitudinal acceleration controller based on a neural network inverse model of the control object is being developed. The advantages of the neural network approach to the inverse model in comparison with classical control theory methods are discussed. Moreover, the paper describes an approach to data collection and processing for training an artificial neural network car longitudinal acceleration controller. A metric for evaluating the quality of the acceleration controller is proposed. The dependencies between the parameters of an artificial neural network controller and the quality of control are revealed.