Taguchi method since 1980 is used as an effective way to optimize the design process engineering tests. In this paper by using of taguchi method optimal conditions of the mixed convection and entropy generation in a square cavity filled with Cu-water nanofluid is analyzed. For this purpose a L16 (43) orthogonal taguchi array is used. Discretization of the governing equations were achieved through a finite volume method and solved with SIMPLE algorithm. The effect of Richardson number (0.1-100 ), the volume fraction of copper nanoparticles (0-10%) and the wavelength of the wavy surface (0- 1) as an effective parameters for analyzing in four levels are considered. This analysis was performed for fixed Grashof number 104. The results show that the mean Nusselt number decreases by increase of the Richardson number, the volume fraction of nanoparticles and the wavelength of the wavy surface. It is found that the Flat plate (for wavy surface with the wavelength 0) and the volume fraction 0% in the Richardson number 0.1 is optimal design for heat transfer while the geometry with Ф=5%, Ri=100 and λ=0.25 is optimal design for entropy generation. Finally for maximum heat transfer and minimum entropy generation the geometry with Ф=0%, Ri =1 and λ=0.25 can be considered as an optimal design.