Development of molecular diffusion to convective fingering is theoretically studied. Linear stability analysis of the Boussinesq perturbation equation including cross-diffusion terms was carried out for a ternary system. The theory describes a fluctuation growth process where the gravitationally stabilized fluid layers at initial are developed to the convective motion by the diffusion of solute. Onset time as well as onset condition of the fluctuation growth is derived. A theory to treat the steady fingering is also presented. A condition to stabilize the fingering flow is derived for the case that the intermolecular diffusion coefficients cannot be neglected.