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As one of steering systems, the steer-by-wire (SbW) system plays a significant role in the automobile. This paper investigates the study of the adaptive discrete-time neural network (NN) steering tracking control of the SbW system based on angular velocity observer. First, the continuous second-order SbW system is discretized by the Euler approximation approach. Before the control design, an adaptive discrete-time angular velocity observer is constructed to estimate the value of angular velocity signal. Then, an adaptive discrete-time control via a backstepping scheme is proposed to achieve the exact steering tracking performance, where the unknown nonlinear function, as well as the control coefficient, are incorporated into the lumped uncertainty and approximated by one NN. The main advantages of the proposed control scheme can be concluded that: (1) without using the exact prior knowledge of system uncertainty and angular position signal, the discrete-time tracking control is achieved and (2) the noncausal problem is overcome without transforming the original system into a predictor form. Finally, the Lyapunov stability theory shows that the tracking error converges to a small neighborhood of zero. Simulations and experiments illustrate the effectiveness and superiority of the proposed adaptive discrete-time NN control.