On the basis of a new dynamic linearization technology along the iteration axis, a dual-stage optimal iterative learning control is presented for nonlinear and non-affine discrete-time systems. Dual-stage indicates that two optimal learning stages are designed respectively to improve control input sequence and the learning gain iteratively. The main feature is that the controller design and convergence analysis only depend on the I/O data of the dynamical system. In other words, we can easily select the control parameters without knowing any other knowledge of the system. Simulation study illustrates the geometrical convergence of the presented method along the iteration axis, in which an example of freeway traffic iterative learning control is noteworthy for its intrinsic engineering importance.