In this paper we present a recurrent neural network for global asymptotic tracking control of discrete-time time-varying nonlinear affine systems with disturbances. The objective is to control the system so that its output can track, from any initial point, an exogenous reference output generated by a known time-varying dynamics. First, we extend the dissipative inequality to a composite system combining the original system and the exogenous reference system. This composite system is not required to have an equilibrium point. Then, by choosing an appropriate time-varying quadratic storage function, the extended dissipative inequality leads to a group of linear matrix inequalities. This group of linear matrix inequalities is mapped to several convex optimization problems. To solve these convex optimization problems, a gradient flow system is developed. In addition, an augmented gradient flow system is carefully proposed to avoid the complicated computation of matrix inverses. A recurrent neural network is designed to realize this augmented gradient flow. At each time step, the recurrent neural network generates a desired control input based on the present state and the system model. The effectiveness and characteristics of the proposed neural controller are demonstrated by simulation results.