For the uncertainty in a class of iterative learning control(ILC) systems, a linear iterative extended state observer(LIESO) in the iterative domain is  resented based on the thought of extended state observer in time domain. This LIESO can estimate explicitly the uncertainty of the ILC system ccording to the tracking error during the process of iterations. The ILC algorithm based on the estimation of the uncertainty is presented, whose convergence is proved by using Lyapunov-like approach. Simulation results show the effectiveness of the proposed ILC algorithm and the iterative learning efficiency can be improved  to much by using LIESO.