In the present study laminar transition to oscillatory convection of cold water in a vertical annulus of aspect ratio 8 and radius ratio 2 is investigated by direct numerical simulations for two values of density inversion parameter, theta(m) = 0.4 and 0.5. The vertical walls of the annulus are maintained at constant but different temperatures, while the horizontal walls are assumed adiabatic. Numerical results manifest that the buoyancy-driven flow in the annulus experiences a Hopf bifurcation into a periodic oscillation regime at the critical Rayleigh numbers, which are dependent on the density inversion parameter. The critical Rayleigh number for theta(m) = 0.4 is found to be more than two times of that corresponding to theta(m) = 0.5. Nature of the transition has also been identified by examining the contributions made by the flow shear and/or the buoyancy force to the generation of fluctuating kinetic energy for the self-sustained oscillatory convection in the annulus.