A compact complex manifold M is called a hyperelliptic manifold (for brevity, an h-manifold) if M has a finite unramified covering manifold which is a complex torus. The classification of h-manifolds was established earlier by Italian geometers, when the dimension is 2. We shall study here the structure of higher dimensional h-manifolds. Though there are some new phenomena which cannot occur in the class of surfaces, most of their results can be generalized to higher dimensional case under certain conditions.