In this paper, thermal blooming of high power laser affected by the convective wind has been simulated numerically and studied. Turbulences are simulated with the RANS/LES hybrid method, coupled with the J-B model. The duel time steps method is used for solving unsteady flow problems. The wave optics method is adopted to simulate beam propagation through both flow field and free space. Based on far field spot, qualitative and quantitative analysis has been carried out. Thermal blooming of Gauss beam with power of 0.1 MW and diameter of 0.1 m, affected by the convective wind at different velocities as follows 1, 5 and 10 m/s, has been investigated. Results show that thermal blooming affected by the wind is unsteady. The lower velocity of the convective wind, the stronger thermal blooming. And especially which of the velocity of 1 m/s is the strongest and aberration of whose far field spot is the most severe. The unsteady property of thermal blooming is more visible as the velocity is lower. For example, thermal blooming at the velocity of 1 m/s is still changing in 5 s, but those at the 5 m/s or 10 m/s have trended to steady state after 3 s.