In this paper, the effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a cavity with a linearly heated wall has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10(4) and 10(5)), Hartmann number (Ha = 0, 15,30 and 60) and power-law index (n = 0.5-1.5) as the magnetic field is applied horizontally. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. The magnetic field decreases heat transfer in different power-law indexes generally. The increment of the magnetic field power declines the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra = 10(4) provokes heat transfer to increase with the enhancement of power-law index. At Ra = 10(5), the heat transfer falls with the rise of the power-law index for Ha = 15 and 30 as the effect is weakened by the increase of Hartmann number significantly. However, the increase in power-law index augments heat transfer at Ha = 60. (C) 2014 Elsevier B.V. All rights reserved.