The spatial distributions of macroscopic parameters such as density, bulk velocity and temperature of the metal vapor have influences on the photo ionization yield of target isotope and the utilization ratio of material, which is related to the separation efficiency and the cost of atomic vapor laser isotope separation. To study this problem more practically, a system of binary gas Bhatnagar-Gross-Krook (BGK) model equations, which describe both the metal vapor and the background gas, is established. The physical characteristics are dealt with by dimensionless method for simplifying the calculations. The model equations are discretized by one-order upwind difference and then are solved by iteration method for obtaining stable results. The computational grids are adjusted to the flow field in order to acquire modest computational cost and accurate result simultaneously. Non-uniform grids in the phase space and in the velocity space are constructed to match the macroscopic parameter gradient and the form of the velocity distribution, respectively. The macroscopic parameters in the cases of different background gas densities, temperatures of tail plate and absorptivities are obtained for studying the influence of the background gas. The results show that with the increase of density of the background gas, the density and temperature of the metal vapor increase, the bulk velocities in the x and z$ direction decrease obviously in the domain far from the evaporation source, while the macroscopic parameters that are close to the evaporation source hardly change. As a result, the evaporation rate is not affected. Meanwhile, a circulation of the background gas is driven by the metal vapor, which in turn affects the diffusion of the metal vapor. Besides, as the temperature of tailing plate rises, the influence of the background gas on the macroscopic parameters of the metal vapor weakens. However, the rise of the temperature of tail plate leads the absorptivity of metal vapor to decrease, which enlarges the influence of the background gas. Therefore, it is appropriate to adjust the temperature of the tail plate based on the relationship between the absorptivity of metal vapor and the temperature. The results of theoretical calculation can serve as a reference for designing the vacuum and laser spot of the separation device.