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The urea-water-solution based selective catalyst reduction (SCR) system is one of the effective devices for reduction of NOx from diesel engines. In an effort to understand the various levels of oscillation observed in the NOx measurement downstream of a SCR in which the urea dosage is controlled by a crankshaft-link pump, a zero-dimensional dynamic SCR model is developed in this paper based on conservation of mass. The model contains three states including the concentrations of NOx and ammonia in the SCR and the surface coverage rate of the catalyst. The temperature-dependent reactions considered in the model include the adsorption, desorption and oxidation of ammonia and the NOx reduction with the reaction constants provided by the catalyst company. The dynamic SCR model is validated both at steady state and during transient under various engine operating conditions and urea dosing rates.