In this paper, double diffusive natural convection of non-Newtonian power-law fluids in an inclined porous cavity in the presence of Soret and Dufour parameters has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). This study has been performed for the certain pertinent parameters of thermal Rayleigh number (Ra-T = 10(4) and 10(5)), Darcy number (Da =10(-4), 10(-3), and 10(-2)), power-law index (n = 0.6-1.4), Lewis number (Le = 2.5 and 5), inclined angles (theta = 0 degrees, 40 degrees, 80 degrees, and 120 degrees), 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 Darcy number causes heat and mass transfer to rise for different power-law indexes. At Da =10-4, the heat and mass transfer increase with the augmentation of the power-law index in the absence of the Soret and Dufour parameters. The rise of the inclined angle from theta = 0 degrees to 40 degrees and from theta = 80 degrees to 120 degrees provokes heat and mass transfer to augment. As the Soret and Dufour numbers equal zero, the heat transfer enhances with the increment of the power-law index at Da = 10(-3). 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 thermal Rayleigh numbers. In some cases, the augmentation of Soret and Dufour parameters alter the behavior of heat and mass transfer against the alteration of the power-law index. (C) 2015 Elsevier Ltd. All rights reserved.