A comprehensive three-dimensional modeling for a single channel of SCR monolith reactor is performed with the laminar flow of viscous gas by the SIMPLE algorithm. The main advantage of this modeling approach is that the processes in the gas phase, washcoat layer and solid substrate are calculated simultaneously by a three-dimensional steady-state simulation. The detailed simulation of SCR monolith reactor may help to understand the complex interactions between various physical and chemical processes that occur in the reactor channel. The washcoat layer is represented by a porous medium. The non-isothermal diffusion and reaction processes are calculated in the waschoat layer by suppressing the convective term of the species transport equation. The effects of pore diffusion and mass transfer on the gas phase which usually lumped into the gas-solid mass and heat transfer coefficients are directly calculated by this fully distributed model. Square channel monolith is selected as an analytical domain. The symmetrical configuration of grid is considered to reduce the computational effort. The modeling is performed by solving the three-dimensional Navier-Stokes, mass conservation, chemical-thermal enthalpy and species transport equations. Eley-Rideal mechanism with the first-order kinetic of NO reduction and NH₃ oxidation is also considered in this study. The processes of NO reduction and NH₃ oxidation by the ammonia gas as a reducing agent are calculated in the source term of the species transport equation. Temperature-dependent gas transport and mixture properties are employed in this simulation. This model allows fully predictions on the SCR monolith performance under diffusion-limited and temperature-dependent conditions. The reactor performances in this simulation result at high and low temperature ranges are calculated and compared with the experimental ones. Also, an effectiveness factor profile obtained from the simulation is compared with the theoretical one.