In 1897, J. Hadamard proved a result about compact, locally strictly convex surfaces in the Euclidean space R3 showing that such surfaces are embedded and homeomorphic to the sphere. Since then many generalizations were made adapting the assumptions about the curvature and considering new spaces in which these surfaces could be immersed so that analogous results were obtained. Following this context, this work generalizes a result of Hadamard-Stoker type to locally convex hypersurfaces immersed in Hn×R. We prove that every complete connected hypersurface immersed in Hn ×R with positive second fundamental is embedded, homeomorphic to the sphere Sn or to Rn, and in the second case we study the behavior of the end.