With the development of the vehicle and Diesel engine technology, the selective catalytic reduction (SCR) technology has been paid more attention recently, which is one of the most effective approaches for reducing the nitrogen oxides (NOx) emissions of Diesel engine exhaust. The control strategy of the ammonia coverage ratio of SCR catalyst is vitally important, which directly influences the NOx reduction efficiency and ammonia leakage. To solve such a challenging task, some assumptions are given firstly based on the understanding of the SCR nonlinear dynamic characteristics, and then the SCR nonlinear model is established by the Continuous Stirred Tank Reactor (SCTR) method. The ammonia storage characteristics are studied based on the established model. Then, the stability and observability of the SCR model are analyzed. For the unmeasurable ammonia coverage ratio and storage capacity of catalyst, a state observer based on the extended Kalman filter (EKF) is proposed. The structure of the closed-loop control system and the corresponding model predictive control (MPC) are designed to improve the robustness of the closed-loop system. The SCR test bench performed on the European Steady Cycle (ESC) and European Transient Cycle (ETC) operating condition is performed for the experimental validation of the control strategy. Meanwhile, a comparison between the proposed method and a feedforward control strategy based on MAP is provided to demonstrate the advantage of this closed-loop feedback control method based on EKF and MPC. The experimental results show that the closed-loop control system can effectively reduce the Diesel NOx emissions and avoid the secondary pollution caused by the ammonia leakage which is applicable to the actual Diesel SCR aftertreatment system.