In this manuscript the influence of local thermal non-equilibrium state on double-diffusive natural convection in a square cavity filled with fluid-saturated porous medium has been addressed numerically. The two dimensional steady state flow is induced due to maintenance of constant temperature and concentration on the vertical walls and insulation of both horizontal walls of the cavity. Non-Darcy (Darcy-Brinkman-Forchheimer) model has been taken and the complete governing equations are solved by standard SIMPLER algorithm. A comparative study of the effect of the presence of Brinkman term in the momentum equation showed that results under the Darcy model are very close to those for the non-Darcy Brinkman model for relatively low permeable medium (e.g., in this study Da = 10(-4)). From our experiments it has been found that the impact of Lewis number (Le) on the average heat transfer rate of fluid (Nu(f)) and solid (Nu(s)) as well as on the thermal distribution of fluid and solid is not straightforward. It depends on the buoyancy ratio (N) and the value of inter-phase heat transfer coefficient (H). However, Le increases the average mass transfer rate (Sh). Also, for each Le there exist a point in the domain of N where Nu(f) is minimum. Similar points also exist for Nu(s) and Sh. In general, these points are different and depend on the LTNE state parameters, except at Le = 1. For any relatively large value of H, when almost thermal equilibrium state is achieved, the point at which Nu(f) and Nu(s) are minimum is same due to similar thermal distribution of fluid and solid. Also, it has been found that, for the buoyancy aided flow (N > 0), the increase in H up to a threshold value (H-0) decreases Sh as well as Nu(f) but increases Nu(s). The H-0 is found to be a decreasing function of the porosity scaled thermal conductivity ratio (gamma) of fluid and solid phases. Overall, the impact of LTNE state on the heat transfer rate and thermal distribution is significant but it is negligible on the mass transfer rate and solute distribution. (C) 2014 Elsevier Ltd. All rights reserved.