In this article, an echo state network (ESN)-based backstepping adaptive iterative learning control scheme is proposed for nonlinear strict-feedback systems performing the same operation repeatedly over a finite-time interval. Different from most of the output tracking approaches, an error-tracking approach is presented using the backstepping technique, such that the tracking error can follow a prespecified error trajectory without any requirement on the initial value of system states. Then, a novel Lyapunov function is constructed to deal with the unknown state-dependent gain function of the controller design. The uncertain nonlinearities are approximated by employing ESNs with simple feedback structures, and the weight update laws are developed by combining the parameter adaptation in the time domain and iteration domain. Moreover, the proposed control scheme is further extended to handle the strict-feedback systems with input saturations. Through the Lyapunov-like synthesis, the closed-loop stability and error convergence of the proposed error-tracking control scheme are analyzed in the presence of the approximation errors. Numerical simulations are provided to verify the effectiveness of the proposed scheme.