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. A periodic modulation of the urea dosing rate is adopted to simulate the periodic urea supply resulted from the reciprocating motion of the crankshaft-link pump. The simulation results exhibit similar oscillatory behaviors in the NOx concentration as observed in the experimental measurement, which is further analyzed and explained based on the nonlinear characteristics between the downstream NOx and the ammonia dosage. Based on the interpretation of the oscillatory NOx signal, an algorithm for identification of the cross-sensitivity of the smart NOx sensor to ammonia is proposed.