The use of 3-D computational fluid dynamics (CFD) is proposed to simulate the conjugate conduction-convection of heat transfer problems in eccentric annularfinned tube heat exchangers. The numerical simulation results allow us to evaluate the heat transfer coefficient over fin surfaces, the fin efficiency and the pressure drop. The aim of the present paper is to determine the optimum tube position in the circular fin that maximizes heat dissipation and minimizes pressure drop. In addition, this study analyzes the effects of fin spacing and fin tube diameter on heat transfer and flow characteristics for a range of Reynolds numbers, 4500≤Re≤22500. A satisfactory qualitative and quantitative agreement was obtained between the numerical predictions and the results published in the literature. For small fin spacings, the eccentric annular finned tube is more efficient than the concentric one. Among the cases examined, the average heat transfer coefficient of the eccentric annular-finned tube, for a tube shift St =12 mm and a Reynolds number Re = 9923, was 7.61% greater than that of the concentric one. This gain is associated with a 43.09% reduction in pressure drop.