In this article, mixed convection heat transfer is numerically studied in a vertical eccentric annulus. For this purpose, full Navier-Stokes equations along with energy equations are solved in a 3-D orthogonal grid using a bipolar cylindrical coordinate system and finite-volume method based on the SIMPLE algorithm. To investigate the flow and heat transfer in the presence of gravity, the inner wall of the annulus is kept at a constant temperature while the outer wall is assumed to be insulated. The effect of different governing nondimensional parameters consisting of dimensionless eccentricity (E), radius ratio (N), and mixed convection parameter (Gr/Re) on the flow and temperature field are studied in detail. The numerical results obtained are in good agreement with the previous numerical works. Furthermore, the flow and heat transfer field in the presence of internal longitudinal fins on the inner wall of the annulus are studied compared with the finless case. The amount of augmented heat transfer due to internal fins is also discussed.