Aging diesel engines on the road require the development of an after-treatment system to meet current emission regulations, and a reduction in NOx (Nitrogen Oxide) is significant. The SCR (Selective Catalytic Reduction) system is the after-treatment system for removing NOx from exhaust gas in diesel engines using NH3 (Ammonia) gas. However, the mixing and conversion process between NH3 and NOx in SCR has not been entirely clarified. That process produces NH3 slip in the catalyst surface; the NH3 slip will make the after-treatment performance worse. This study informs how the UWS (Urea Water Solution) injection controlling method can minimize the NH3 slip in the after-treatment system. For this, the NH3 adsorption and desorption rates are important factors for determining the quantity of UWS injection in the system. The NH3 adsorption rate and desorption rate in the SCR are not significantly affected by engine speed, i.e., the exhaust gas flow rate. However, as the exhaust gas temperature increased, the adsorption rate and desorption rate of NH3 in the SCR increased. Through this, the exhaust gas temperature dramatically affects the NH3 adsorption rate and desorption rate in the SCR. Therefore, if the urea water is injected based on this knowledge that the NH3 adsorption amount in the SCR decreases as the exhaust gas flow rate increases, NH3 slip can be suppressed and a high NOx reduction rate can be achieved. Therefore, if the SCR adsorption and desorption mechanisms are analyzed according to the exhaust temperature and the exhaust flow rate in this paper, it can be used as a reference for selecting an appropriate SCR when retrofitting an old diesel engine car.