We　propose　a　scheme　for　preparation　of　entangled　coherent　states　for　the　motion　of　an　ion　in　a　two-dimensional　anisotropic　trap.　In　the　scheme,　the　ion　is　driven　by　four　laser　beams　along　different　directions　in　the　ion　trap　plane,　resulting　in　carrier　excitation　and　couplings　between　the　internal　and　external　degrees　of　freedom.　When　the　total　quantum　number　of　the　vibrational　modes　initially　has　a　definite　parity,　the　competition　between　the　unitary　dynamics　and　spontaneous　emission　will　force　the　system　to　evolve　to　a　steady　state,　where　the　vibrational　modes　are　in　a　two-mode　cat　state.　We　show　that　the　method　can　be　extended　to　realization　of　entangled　coherent　states　for　three　vibrational　modes　of　an　ion　in　a　three-dimensional　anisotropic　trap.　©　2018　American　Physical　Society.