State estimation is an important problem in distributed parameter system especially with nonlinear dynamics in industrial process. An extended Luenberger observer based on the eigen-spectrum of the system operator is developed in this paper to handle this problem. The distributed parameter system is projected into a finite-dimensional subspace where a low-order ordinary differential equation describing the dominant dynamics of the system is derived. A Luenberger observer extended with a nonlinear part is developed based on that dominant dynamics. A sufficient condition is given in this paper for the convergence of the estimated error. Finally, by applying the developed design method to the temperature estimation of a catalytic rod, the achieved simulation results show the effectiveness of the proposed observer. (C) 2020 Elsevier Ltd. All rights reserved.