Transition of flows in natural convection in a horizontal cylindrical annulus is investigated for the fluid with Pr=0.2. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped eddy flow bifurcates to a time-periodic flow with like-rotating eddies. After the first Hopf bifurcation, however, a reverse transition from oscillatory to a steady flow occurs by the flow pattern variation. Hysteresis phenomenon occurs between the solution branches of up-scan and down-scan stages, and dual solutions with one steady and one oscillatory flow are found. Overall Nusselt of the flows at the flows at the down-scan stage is greater than that at the up-scan stage.