This note is concerned with the robust discrete-time iterative learning control (ILC) design for nonlinear systems with varying initial state shifts. A two-gain ILC law is considered using a 2-D analysis approach. Sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition. It is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete-time ILC.