In　this　paper,　we　show　that　multi-phonon　NOON　states　can　be　generated　in　a　two-dimensional　anisotropic　trapped-ion　system.　In　the　proposal,　two　laser　pulses　are　applied　to　an　ion　along　different　directions　in　the　ion　trap　plane　to　exchange　the　information　between　the　external　and　internal　states　of　the　ion.　Different　from　the　previous　frameworks,　the　proposal　is　outside　the　Lamb-Dicke　regime.　The　distinct　advantage　of　the　proposed　scheme　is　that　the　entanglement　generation　is　deterministic　and　no　measurement　on　the　system　is　required.　Numerical　simulations　show　that　the　fidelity　of　the　prepared　entangled　states　is　strongly　affected　by　Lamb-Dicke　parameters.