In order to understand the nature of thermocapillary convection under microgravity in a differentially heated annular pool with the outer heated container of radius r o =40 mm and the inner cooled cylinder of r i =20 mm, and an adjustable depth d=3-14 mm, we conducted a series of unsteady two-dimensional numerical simulations with the finite volume method. The pool was filled with the 0.65cSt silicone oil (Prandtl number Pr=6.7). With a large enough temperature difference in the radial direction, the simulation can predict oscillatory thermocapillary flows. Hopf bifurcation neutral curve is delineated in the thermocapillary Reynolds number (Re)-aspect ratio (A=(r o -r i )/d) plane. It is found that time-dependent motion is only possible if A exceeds a critical value A c r i which is around 2.29. Streamline and isotherm patterns are presented at different thermocapillary Reynolds number and the aspect ratio corresponding to stationary and oscillatory states.