The coupled thermal and solutal capillary convection subjected to radial temperature gradient in a shallow annular pool with free surface is investigated by using asymptotical analysis and the solution is obtained in the core region. The influences of Soret effect and buoyant force on fluid flow are analyzed. The results show that when the solutal capillary force and the buoyancy induced by the ununiform distribution of solute concentration are not considered, the asymptotic solution is the same as the asymptotic solution of pure thermocapillary-buoyancy convention or thermocapillary convection in a shallow annular pool. The influence of the buoyancy on the fluid flow is slight and the coupled thermal and solutal capillary forces play a dominant role in the convection in shallow annular pool. When the coupled forces are in the same direction, the flow is reinforced. Otherwise, the flows suppress each other.