Employing density functional calculations we predict that SmS undergoes a topological phase transition from the trivial Kondo insulator (KI) black phase to a topological metallic gold phase under hydrostatic pressure. The underlying mechanism is the pressure-induced change of the 4f level from below to above the bottom of the 5d conduction band, leading to a d-f band inversion, a parity sign reversal, and the concomitant change of the topological invariant ν0. This provides a material realization of the topological classification of KIs proposed by Dzero et al.