In this paper, heat transfer and entropy generation on laminar natural convection of non-Newtonian nanofluids in the presence of an external horizontal magnetic field in a square cavity has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The cavity is filled with water and nanoparticles of copper (Cu) while the mixture shows shear-thinning behavior. This study has been conducted for the certain pertinent parameters of Rayleigh number (Ra = 10(4)-10(5)), power-law index (n = 0.6-1), Hartmann number (Ha = 0-90) and the volume fraction has been studied from phi = 0 to 0.04. Results indicate that the augmentation of the power-law index causes heat transfer to drop in the absence of the magnetic field, by contrast, the heat transfer increases with the rise of power-law index in the presence of the magnetic field. The addition of nanoparticle augments heat transfer for multifarious studied parameters. The heat transfer drops with the increase in Hartmann number generally and also affects the power-law index and nanoparticles influences on heat transfer. Augmentation of the volume fraction and Rayleigh number enhance all kinds of entropy generations of heat transfer, fluid friction, and the magnetic field in different studied parameters. The increase in the Hartmann number causes the total entropy generation to drop and affects the influences of the power-law index and the volume fraction on the entropy generations. (C) 2015 Elsevier Ltd. All rights reserved.