The present paper numerically studies two-dimensional steady-state natural convection of non-Newtonian power-law fluid between two eccentric horizontal square ducts with constant temperature. The inner and outer ducts are assumed to be held at hot and cold temperatures, respectively. The conservation equations of mass, momentum and energy are dicretized using finite volume technique based on second order upwind and finally SIMPLE algorithm is utilized to solve the resultant system of equations. The effects of power-law index (0.6 <= n <= 1.4), Rayleigh number (10(3) <= Ra <= 10(6)), aspect ratio (0.25 <= AR <= 0.75), eccentricity (-0.2 <= e <= +0.2) and Prandtl number (10 <= Pr <= 10(3)) on heat and fluid flows are investigated. Also the Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index n from 0.6 to 1.4 the mean Nusselt number that indicates heat transfer rate decreases. It is shown that there is a minimum situation for the Nusselt number versus the eccentricity dependent on the other parameters. Also it is found that varying the Prandtl number almost does not affect heat transfer characteristics except for some cases. (C) 2013 Elsevier B.V. All rights reserved.