Abstract：The concept and clarifications of indoor air stability are validated by a mathematical method. The indoor air stability is classified into three types, that is, stable, neutral, and unstable according to the environmental temperature lapse rate after the mathematical derivation. A physical model is established under different temperature gradients. By use of Computational Fluid Dynamics (CFD) software, the propagation characteristics of NH3 and other indoor pollutants are simulated under the condition of lateral ventilation. The diffusion laws of pollutants with different stabilities are obtained through a numerical simulation. The results show that in the unstable conditions, pollutants can quickly get up to the exit with the up-return and down-supply pollutant ventilation. However, pollutants are easy to accumulate indoors and difficult to exhaust in the stable conditions. Unstable conditions are conducive to the formation and development of turbulence; and stable conditions inhibit the development of turbulence. However at large Reynolds number (at the entry speed of 3m/s), the influence of the stabilities on the dispersal of pollutants is not significant. For different pollutants gases, the stability effect of CO2 is better than that of NH3, as CO2 can not be easily discharged to the outside. At the same time, the instability can be reduced with the decrease of temperature difference along the vertical direction. The stability drops down with the decrease of inversion temperature difference. But the effect degree of environmental temperature on stability is closely related to Reynolds number. This work provides a theoretical basis for the indoor pollutant control strategies.