A new global model for the Martian atmosphere with a vertical domain extending from the surface into the thermosphere (at about 160--180 km) is presented with some preliminary results. The model is a grid point model with a semi-Lagrangian semi-implicit dynamical scheme that is used for weather forecasting by the Meteorological Service of Canada. The physics includes a comprehensive radiative transfer scheme for heating, a boundary and surface layer parameterization. The design of the model allows for different grid configurations that include a globally uniform grid as well as the possibility of zooming over an area of interest with a locally uniform grid. The performance of the model is shown both in global uniform-resolution simulations as well as high-resolution simulations over the Tharsis Montes region. The simulated temperatures are compared with the Thermal Emission Spectrometer's measured profiles and the Mars Pathfinder entry data. Both the agreement with the data and the depiction of known features of the Martian atmosphere indicate that the Global Mars Multiscale Model has a good potential for modeling the atmosphere of Mars.