Using the analogy between the discrete time axis and the iterative learning axis, a new discrete-time adaptive iterative learning control (AILC) approach is developed to address a class of nonlinear systems with time-varying parametric uncertainties. Analogous to adaptive control, the new AILC can incorporate a projection algorithm, thus the learning gain can be tuned iteratively along the learning axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.