Consider the Langevin process, described by a vector (position,momentum) in Rd×Rd. Let O be a C2 open bounded and connected set of Rd. We prove the compactness of the semigroup of the Langevin process absorbed at the boundary of the domain D:=O×Rd. We then obtain the existence of a unique quasi-stationary distribution (QSD) for the Langevin process on D. We also provide a spectral interpretation of this QSD and obtain an exponential convergence of the Langevin process conditioned on non-absorption towards the QSD.