In this work, ballistic phonon transport in atomic chain nanostructures is investigated by atomic nonequilibrium Green's functions and embedded atom method. Bond length and strength modification in atomic chain (low-dimensional structure) was taken into consideration by using bond-order-length-strength correlation premise. We especially focus on the contact interface effects on phonon transmission and thermal conductance. It is found that the contact interfaces between an atomic chain and contact reservoir, i.e., neck region or buffer layers, play an important role in phonon transport. The more buffer layers the less thermal conductance.