This　paper　proposes　a　novel　method　for　motion　field　estimation　in　two　consecutive　LiDAR　scans　with　convolutional　neural　networks　(CNNs)　wherein　object　detection,　point-wise　motion,　and　object-level　motion　are　learned　hierarchically.　In　the　input　stage,　a　unique　mapping　model　serves　to　describe　the　LiDAR　point　cloud　and　its　motion.　In　the　encode　network,　two　input　maps　are　subjected　to　spatial　compression　and　merged　into　a　correlation　layer.　In　the　decode　network,　the　model　outputs　data　encompassing　object　detection,　point-wise　motion,　and　object-level　motion.　Since　existing　ground　truth　datasets　are　not　sufficiently　large　to　train　a　CNN,　we　generate　a　synthetic　Vehicle　Motion　dataset　for　training.　The　set　contains　scenes　with　several　simultaneously　moving　3D　vehicles　recorded　by　a　simulated　LiDAR.　An　experiment　conducted　on　both　real　and　synthetic　datasets　shows　that　the　proposed　method　outperforms　other　state-of-the-art　motion　field　estimation　methods.　(C)　2019　Elsevier　B.V.　All　rights　reserved.