For the fault estimator based on the iterative learning theory, an iterative learning algorithm based on the extended states observer(ESO) is proposed to improve the convergence speed of the virtual fault. In this algorithm, the nonlinear feedback mechanism of the ESO is transplanted to iterative learning processes, that is, the nonlinear function of the current output residual is used to adjust the value of the virtual fault in the next iteration. The theoretical convergence analysis of the proposed fault estimator is proven, based on which some simulation experiments are conducted. The obtained results show the favorable convergence speed and the fault estimation precision of the proposed method.