It is known that every closed oriented 3-manifold is a simple 3-fold branched covering space of the 3-sphere branched along a link. We can regard the branch set with some information as a presentation of the 3-manifold, which we call the covering presentation. In this talk we give a new construction of invariants of 3-manifolds formulated on their covering presentations, and realize the Dijkgraaf-Witten invariant as such an invariant.