Transient kinetics of $NH_3$ adsorption/desorption and of SCR(selective catalytic reduction) of NO with $NH_3$ were studied over vanadium based catalysts, such as $V_2O_5/TiO_2$ and $V_2O_5-WO_3/TiO_2$. In the present catalytic reaction process, NO adsorption is neglected while $NH_3$ is strongly chemisorbed on the catalytic surface. Accordingly, it is ruled out the possibility of a reaction between strongly adsorbed $NH_3$ and NO species in line with the hypothesis of an Eley-Rideal mechanism. The present kinetic model assumes; (1) non-activated $NH_3$ adsorption, (2) Temkin-type $NH_3$ coverage dependence of the desorption energy, (3) non-linear dependence of the SCR reaction rate on the $NH_3$ surface coverage. Thus, the surface heterogeneity for adsorption/desorption of $NH_3$ is taken into account in this model. The present study extends the pure chemical kinetic model based on a powdered-phase catalytic system to the chemico-physical one applicable to a realistic monolith reactor.