In this paper, double diffusive natural convection of non-Newtonian power-law fluids in an open cavity in the presence of a horizontal magnetic field, studying Soret and Dufour parameters has been analyzed by FDLBM (Finite Difference Lattice Boltzmann method). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10(4) and 10(5)), Hartmann number (Ha = 0, 15, and 30), power-law index (n = 0.6, 1, and 1.4), Lewis number (Le = 2.5 and 5), Dufour parameter (D-f = 0, 1, and 5), Soret parameter (S-r = 0, 1, and 5) and the buoyancy ratio (N = -1 and 1). Results indicate that the augmentation of the Hartmann number provokes heat and mass transfer to drop for different power-law indexes. As the Soret and Dufour numbers equal zero, the heat and mass transfer decrease with the increment of the power-law index in different Rayleigh numbers for various Hartmann numbers. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different power-law indexes and Rayleigh numbers. The augmentation of Soret and Dufour parameters alters the behavior of heat and mass transfer against the change of the power-law index. (C) 2016 Elsevier Ltd. All rights reserved.