In many practical distributed parameter systems (DPSs), the states of the systems are required to track a desired trajectory repeatedly over a finite duration. It is hard to design the controllers for the systems to obtain uniformity and repetitiveness of the states simultaneously. In this paper, iterative learning control (ILC) based on the eigenspectrum of the system is proposed for a class of parabolic DPS to tackle this control problem. First, Galerkin's method with the eigenspectrum as the base is applied to the original system to obtain a reduced-order model which exhibits the dominant dynamics of the system. Then, an ILC controller based on the reduced-order model is developed. The stability and convergence of the proposed approach are analyzed and guaranteed under the framework of functional analysis. Finally, simulations on the temperature profile control of a rapid thermal processing system are performed to demonstrate the effectiveness of the developed ILC scheme.