In this paper, laminar mixed convection of non-Newtonian nanofluids in a square lid-driven cavity with a sinusoidal boundary condition has been analyzed by finite difference lattice Boltzmann method (FDLBM). The cavity is filled with water and nanoparticles of Alumina (Al2O3) while the mixture shows shear-thinning behavior. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.001-1), power-law index (n=0.2-1), and the volume fraction (φ=0-0.09) while Grashof number is fixed at Gr=100. Results indicate that the augmentation of Richardson number decreases heat transfer. The fall of the power law index declines heat transfer for different studied Richardson numbers. The addition of nanoparticle augments heat transfer for multifarious studied parameters. The effect of nanoparticle on the enhancement of heat transfer decreases with increase in power-law index. The influence of nanoparticle for different power-law indexes drops as the Richardson number augments.