In this study simulated was the flow field structure around a cubic building under different thermal stratifications, by using the RNG k-ε turbulence model. The simulated results were validated by corresponding wind-tunnel experiment. The results show that CFD simulation can reproduce the separation zones, wake regions and cavity zones when airflow passes the building. When atmospheric condition is stable, the separation zones are relatively small near the top and two sides, and the building impact in the horizontal direction is greater than that in the vertical direction. The changes in turbulence kinetic energy under stable conditions are smaller than those under neutral conditions. In addition, near the top of the building, the magnitude of turbulence kinetic energy under stable conditions is lower than that under neutral and unstable conditions. The effect of atmospheric stability on turbulence kinetic energy is significant. The magnitude of turbulence kinetic energy is usually great near the building because of the interaction between the mechanical disturbance and thermal stability. The effect of thermal stability on turbulence kinetic energy is gradually apparent with increasing downwind distance.