<p>Let <i>M</i> be a finite-volume non-compact complete hyperbolic <i>n</i>-manifold with totally geodesic boundary components. We show that there exists a polyhedral decomposition of <i>M</i> such that each cell is either an ideal polyhedron or a partially truncated polyhedron with exactly one truncated face. This result parallels Epstein-Penner’s ideal decomposition for cusped hyperbolic manifolds and Kojima’s truncated polyhedral decomposition for compact hyperbolic manifolds with totally geodesic boundary components. We take two different approaches to demonstrate the main result in this paper. We also show that the number of polyhedral decompositions of <i>M</i> is finite.</p>