Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows from steady to oscillatory convection is investigated for the fluid with Pr=0.1. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped flow bifurcates to a time-periodic flow with like-rotating eddies. And afterwards, a transition to an oscillatory multicellular flow with a counter-rotating eddy on the top of the annulus occurs. A transition from steady to an oscillatory flow occurs, but dual solutions and hysteresis phenomena are not observed.