  We formulate a new scheme of the Hartree-Fock-Bogoliubov mean-field theory
applicable to weakly bound and pair correlated deformed nuclei using the
coordinate-space Green's function technique. On the basis of a coupled-channel
representation of the quasiparticle wave function expanded in terms of the
partial waves, we impose the correct boundary condition of the asymptotically
out-going waves on the continuum quasiparticle states. We perform numerical
analysis for $^{38}$Mg to illustrate properties of the continuum quasiparticle
states and the pair correlation in deformed nuclei near the neutron drip-line.
