We prove that for a normal projective variety X in characteristic 0, and a base-point free ample line bundle L on it, the restriction map of divisor class groups Cl(X) → Cl(Y) is an isomorphism for a general member Y ∈ |L| provided that dim X ≥ 4. This is a generalization of the Grothendieck-Lefschetz theorem, for divisor class groups of singular varieties.