A mathematic model of aluminum extrusion process using body-fitted grids based finite volume method was studied and established in this paper. The basic goverment equations of the finite volume method were built, body-fitted grids were used to mesh computational region, basic goverment equations were discretized on body fitted grids directly, so complex coordinate conversion was avoided by no use of aptamer coordinate system. Initial conditions, boundary conditions and calculation processes of aluminum extrusion process finite volume method were studied and established, a program had been written based this model and a typical process of aluminum extrusion was simulated, amount of physical fields such as velocities, effective stress and effective strain rate etc. were obtained, the results were compared with that simulated by finite element method, so the feasibility and exactness of the mathematic model is proved.