This article numerically studies entropy generation due to natural convection in a rectangular cavity with circular corners. In this work, in order to solve the governing equations, an explicit finite-volume procedure and a time-marching method are utilized. Also, instead of the conventional algorithms of SIMPLE, SIMPLEM, and SIMPLEC, an artificial compressibility technique is applied for coupling the continuity to the momentum equations. Entropy generation, as a representation of irreversibility and efficiency loss in engineering heat transfer processes, is analyzed in detail. In this work, effects of the radius of walls corner, Rayleigh number, and distribution ratio on total entropy generation, Nusselt number, and Bejan number are also evaluated. The results show that entropy generation decreases with the increase of the radius of the walls' corner and increases with the increase of Rayleigh number, aspect ratio, and irreversibility ratio.