Double-diffusive natural convection in fluid-saturated porous medium inside a vertical enclosure bounded by finite thickness walls with opposing temperature, concentration gradients on vertical walls as well as adiabatic and impermeable horizontal ones has been performed numerically. The Darcy model was used to predict fluid flow inside the porous material, while thermal fields are simulated based on two-energy equations for fluid and solid phases on the basis of a local thermal non-equilibrium model. Computations have been performed for different controlling parameters such as the buoyancy ratio , the Lewis number Le, the anisotropic permeability ratio , the fluid-to-solid thermal conductivity ratio , the interphase heat transfer coefficient , the ratio of the wall thickness to its height , the wall-to-porous medium thermal diffusivity ratio , and the solid-to-fluid heat capacity ratio . Thus, the effects of the controlling parameters on heat and mass transfer characteristics are discussed in detail. Moreover, the validity domain of the local thermal equilibrium (LTE) assumption has been delimited for different set of the governing parameters. It has been shown that Le has a noticeable significant effect on fluid temperature profiles and that higher values lead to a significant enhancement in heat and mass transfer rates. Moreover, for higher , , or values and/or lower values, the solid and fluid phases tend toward LTE.