In this study, stability of unsteady mixed convection in a horizontal annulus between two concentric cylinders was investigated numerically. The surfaces of the cylinders were considered to be at fixed temperatures and it was assumed that the hot inner cylinder is rotating at a constant angular velocity. The buoyancy forces were formulated utilizing the Boussinesq approximation. The governing equations of fluid flow and heat transfer in the annulus were solved with a finite element method for different values of the geometric (radius ratio) and transport parameters (Rayleigh number and Reynolds number). Development of the convective flow and heat transfer was expressed by the average Nusselt number for the outer cylinder. The results show that, for a narrow gap annulus, convective flow induces flow bifurcation and becomes unstable for high values of the Rayleigh number. Flow becomes more unstable with an increase in the Reynolds number. For a wide gap annulus, flow is stable for all values of the Rayleigh number if the rotation effects are small. On the other hand, convective flow becomes unstable for the modest and high values of the Ra number with an increase in the Re number.