The effect of local thermal non-equilibrium on the onset of double-diffusive convection in a porous medium consisting of two horizontal layers is studied analytically. Linear stability theory is applied. Variations of permeability, fluid conductivity, solutal diffusivity, solid conductivity, interphase heat transfer coefficient, and porosity are considered. It is found that with the introduction of double diffusion, the heterogeneity of porosity now has a major effect, comparable to the effects of heterogeneity of permeability and fluid conductivity. The general results are obtained by using a one-term Galerkin approximation. We validate this approximation by comparing these results with those obtained by using a highly accurate numerical solver. We thus established the accuracy of a one-term Galerkin approximation for stability analysis of a complicated convection problem.