This study uses the linear stability analysis to understand the transition characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr=0.011) fluid. The annular pool is heated from the outer cylindrical wall and cooled at the inner wall. The bottom and top surfaces are adiabatic. The results show that with the increase of the aspect ratio, the critical Marangoni number and the critical wave number decrease. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. With the increase of the radius ratio, the critical Marangoni number decreases slightly, while the critical wave number increases.