We intend to develop an atmospheric meso-scale numerical model, which is expected to suitably treat the steep topography and complex objects on the earth's surface with a finer resolution. In this work, the finite volume method(FVM) in conjunction with the SIMPLER(Semi-Implicit Method for Pressure-Linked Equation Revised) algorithms is used for calculations of the unsteady, three-dimensional, compressible Navier-Stokes equations on a staggered grid. Abandoning the customary terrain-following normalization, we choose the Cartesian coordinate in which the height is used as the vertical one. Blocking-off method is introduced to handle all of the steep topography and complex objects above the earth's sea-mean level. For the spatial and temporal discretizations, higher-order upwind convection scheme is employed, and fully time implicit scheme is utilized. As a preliminary test, the model has been run on flows over a cube mounted on surface. Result of simulations is present, which shows the potential of our proposed approaches for the next-generation atmospheric meso-scale model development.