This article reports the numerical study of natural convection in a differentially heated cylindrical annular enclosure with a thin baffle attached to inner wall. The inner and outer walls of the annulus are respectively maintained at higher and lower temperatures, whereas the top and bottom walls are thermally insulated. Using an implicit finite difference technique, the effects of baffle size and location on natural convection has been investigated for different Rayleigh numbers and radius ratios by fixing the Prandtl number at 0.707. Through the detailed numerical simulations, we have successfully captured the important effects of baffle size and location on the flow pattern and heat transfer rate. It has been found that the size and location of baffle modify the flow pattern and heat transfer rate in a completely different conducts. The numerical results corroborates that the average heat transfer rate increases with the Rayleigh number, radius ratio, baffle position, but decreases with baffle length. Further, it has been observed that it is possible to enhance or suppress the flow circulation and heat transfer rates by a proper choice of baffle size and location, and Rayleigh number.