To study the linear stability of the buoyancy-thermocapillary convection in a small Prandtl number liquid bridge， the buoyancy-thermalcapillary convection stability of silicon liquid bridge with Pr=0.011 is studied under constant gravity combined with two different heating methods， and compared with the flow stability of liquid bridge under zero gravity（real-world applicability）. The results show that：The instability type of flow in the presence of gravity and zero gravity is static instability with wave number 2， and the instability of flow is caused by shear mechanism. The introduction of gravity has not changed the instability mode and mechanism of flow. While gravity exists， different heating directions have different effects on the flow stability of the liquid bridge. When considering the free surface deformation， the stability of the liquid bridge flow under bottom heating is stronger than that under top heating， and the opposite is true when not considering the deformation of free surface. The stability of liquid bridge flow in the presence of constant gravity is not always stronger than that in zero gravity， which is related to the heating mode. When Bo ≤ 0.34 （bottom heating） or Bo ≤ 3.05 （top heating）， the effect of gravity on the flow stability of the liquid bridge can be neglected.?