The classical Nakai–Moishezon–Kleiman ampleness criterion characterizes ample line bundles on a projective variety as those which have positive intersection against all subvarieties. In a groundbreaking paper, Demailly and Paun proved a vast generalization of this result, which holds for all closed real (1,1) classes on a compact K ̈ahler manifold. Generalizing the result of Demailly–Paun, we establish Nakai–Moishezon type criterion on a singular complex compact variety under some geometric conditions.