In this paper, laminar mixed convection of shear-thinning fluids in a square lid-driven cavity with sinusoidal boundary conditions under the combined buoyancy effects of thermal and mass diffusion has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). This study has been conducted for the certain pertinent parameters of Richardson number (Ri= 0.00062-1), Lewis number (Le= 5 and 50), power-law index (n= 0.2-1) as the buoyancy ratio is studied from N= -10 to 10. Results indicate that the augmentation of Richardson number decreases heat and mass transfer. The fall of the power law index declines heat and mass transfer at Ri= 0.00062 and 0.01. At Ri= 1, the heat and mass transfer rises with the increment of power-law index for buoyancy ratios of N= 1. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri= 1. The growth of Lewis number enhances the mass transfer as it alters the effect of power-law index on the mass transfer.