This article aims to solve the optimal tracking problem (OTP) for a class of discrete-time (DT) nonlinear systems with completely unknown dynamics. A novel data-driven deterministic approximate dynamic programming (ADP) algorithm is proposed to solve this kind of problem with only input-output (I/O) data. The proposed algorithm has two advantages compared to existing data-driven deterministic ADP algorithms for the OTP. First, our algorithm can guarantee optimality while achieving better performance in the aspects of time-saving and robustness to data. Second, the near-optimal control policy learned by our algorithm can be implemented without considering expected control and enable the system states to track the user-specified reference signals. Therefore, the tracking performance is guaranteed while simplifying the algorithm implementation. Furthermore, the convergence and stability of the proposed algorithm are strictly proved through theoretical analysis, in which the errors caused by neural networks (NNs) are considered. At the end of this article, the developed algorithm is compared with two representative deterministic ADP algorithms through a numerical example and applied to solve the tracking problem for a two-link robotic manipulator. The simulation results demonstrate the effectiveness and advantages of the developed algorithm.