In this paper, mixed convection of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. The Prandtl number is fixed at Pr=1. This study has been performed for the certain pertinent parameters of Richardson number (Ri = 0.001, 0.01, and 1), buoyancy ratio number (Nr = 0.1, 1, and 20), power-law index (n = 0.2-1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (Nt = 0.1, 0.5, 1), and Brownian motion parameter (Nb = 0.1, 1, 5). Results indicate that the augmentation of the power-law index causes heat and mass transfer to drop at Ri = 0.001 and 0.01. The drop of Richardson number from Ri = 1 to 0.001 enhances teat and mass transfer for various power-law indexes. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorates mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. (C) 2017 Elsevier Ltd. All rights reserved.