Numerical analysis has been carried out for two-dimensional steady and unsteady mixed convection in the annulus between co-rotating horizontal cylinders with a heated inner cylinder. The ratio of annulus gap($sigma$) is taken from 1 to 10 and the order of mixed-convection parameter B(=Gr/(1+Re)$^2$) varies from 10$^4$to $10^0$. The flow patterns over this parameter range are steady multicellular, oscillatory multicellular or steady unicellular. The addition of co-rotating of both cylinders stabilizes the flow in the annulus and weakens the unsteadiness. Even in the large values of rotating parameter such as of $10^0$/($sigma$=2) and 10$^2$($sigma$=10), the flow pattern becomes asymptotic to the steady unicellular flow, like as in the rigid-body rotating flow.