This paper studies the influence of buoyancy convection caused by the laser energy absorbed by air during the propagation of high-power laser in a closed channel on the thermal blooming effect. A physical model of the thermal blooming effect under buoyancy convection is constructed. Two factors that affect beam quality, namely heat conduction and convection heat transfer, are analyzed by a numerical calculation method. It is found that buoyancy convection can reduce the thermal blooming effect in the closed channel and cause beam centroid drift. The far-field spot shape, beam quality, and spot centroid drift of array beams with different arrangements are studied. The results show that the buoyancy convection under the interaction among the array beams is greater, and the reduction of the thermal blooming effect is more severe. The conditions of beams at different positions with different arrangements are different. Beam quality and centroid shift can be optimized by choosing the appropriate arrangement. In addation, we verified that axial wind can be adopted to suppress the thermal blooming effect. The results show that buoyancy convection can promote the reduction of the thermal blooming effect. When the axial wind increases, the thermal blooming effect vanishes, and the influence of buoyancy convection gradually disappears.