In this paper, entropy generation of associated with the natural convection of non-Newtonian nanofluid, using the Buongiorno's mathematical model in an inclined cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10(4) and 10(5)), inclined angle (theta = 0 degrees, 40 degrees, 80 degrees, 120 degrees), buoyancy ratio number (Nr = 0.1, 1, and 4), power-law index (n = 0.4 - 1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (Nt = 0.1, 0.5, 1), and Brownian motion parameter (Nb = 0.1, 1, 5). The Prandtl number is fixed at Pr = 1. The Results indicate that the augmentation of the power-law index enhances various entropy generations in different Rayleigh numbers and inclined angles. The lowest total entropy generation was observed in the inclined angle of theta = 0 degrees in different Rayleigh numbers. In addition, the highest values of Bejan number was found in the inclined angle of theta = 0 degrees in various Rayleigh numbers. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility. (C) 2016 Elsevier B.V. All rights reserved.