The liquid layer thickness plays an important role in the thermocapillary convection of liquid layer system.However,most of previous researches focused on the convention caused by a mono-directional temperature gradient.In this paper,the effect of the liquid layer thickness on the thermocapillary convection in an annular twolayer system subjected to a bidirectional complex temperature gradient is investigated by a set of two-dimensional numerical simulations.In the simulations,the system bottom is heated by following a linear temperature profile,and the free surface convects with outer space.Moreover,the liquid layer thickness ratio H_r changes from 0.1 to 0.9,the range of the radial temperature difference Re is 0 ～ 1.5 ×10⁶,and the thickness radial ratio Γ is 0.1,0.2,0.3.The results show that ( 1) when Re is smaller,there exists an axisymmetric steady flow,and the thermocapillary convection decreases with the increase of H_r ; ( 2) an unsteady multi-cellular flow occurs as Re increases and then exceeds a critical value,and both the amplitude and the convection decrease with the increase of H_r ; ( 3) the critical value changes with H_r in a non-monotonic way; and ( 4) when Hr locates between 0.5 and 0.7,the critical Re is always the biggest at different Γ,and the system is in the most stable state.