A mathematical modeling of $NO_x$ reduction in $NH_3$-SCR process is conducted. The present deterministic model solves one-dimensional conservation equations of mass and species concentrations for channel flows and the catalytic reaction. NO and NO_2$ reactions by the vanadium catalyst in the presence of $NH_3$ are calculated with the rate expressions of Langmuir-Hinshelwood scheme. The modeling was validated with extensive empirical data regarding $NO_x$ reduction efficiency. Analysis of De-$NO_x$ sensitivity conducted with regard to oxygen and water yielded highly accurate prediction over a wide range of $NO_2/NO_x$ ratios from 0 to 1 in a temperature range of $200^{circ}C{sim}550^{circ}C$. The $NO_x$ reduction largely depends on $NO_2/NO_x$ ratio at temperatures lower than $300^{circ}C$. NO reduction efficiency is significantly augmented with increasing in $NH_3$/NO ratio at higher temperatures, whereas rather insensitive to the $NH_3$/NO ratio at lower temperatures.