This paper is devoted to design a model-based boundary optimal controller for selective catalytic reduction system. The mathematical model consists of coupled parabolic-hyperbolic PDEs with an ODE. The main objective is to manipulate the ammonia gas at the inlet of the SCR in order to reduce the amount of NOx and ammonia slip as much as possible. The augmented infinite-dimensional state space representation has been used in order to solve the corresponding linear-quadratic control problem. The dynamical properties of both the linearized system and its augmented version have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilizable and detectable C-0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. An algorithm has been developed to describe the steps of solving the Riccati equation. Numerical simulations for the closed-loop system have been implemented to show the controller performances. (C) 2018 Elsevier Ltd. All rights reserved.