Entropy generation and Laminar Natural convection of Cu-water Nano fluid near density maximum of water (non-Boussinesq approximation) in a two-dimensional horizontal concentric cylindrical annulus is investigated numerically. The governing equations based on the non-Boussinesq homogenous model are solved on a non-uniform ring type mesh using a pressure-based finite volume method. The calculation is performed for Ra=10⁵ and nanoparticle volume fraction from 0 to 0.08. Numerical results are presented in the terms of streamlines, isotherms, velocity vectors and local and average Nusselt number. Aso contours of local entropy generation and average entropy generation are presented. It is found that the density inversion and the presence of nanoparticles both play a significant role in the flow field structure and heat transfer characteristics. It can be concluded that Boussinesq approximation gives rise to the higher average heat transfer rate and entropy generation as compared to non-Boussinesq approximation. In addition, the average Nusselt number decreases as the volume fraction of nanoparticle increases. Finally, the present numerical results verify the determining effect of the density inversion of water on the convection character because of the formation bi-cellular structure.