In [20], it was shown that there are no warped product semi-slant submanifolds of Kaehler manifolds. In this paper, we show that there exists a class of non-trivial warped product semi-slant submanifolds of a locally product Riemannian manifold contrary to Kaehlerian case. Then, we give a characterization, an example and investigate the geometry of warped product semi-slant submanifolds in a locally product Riemannian manifold.