Many　factors　influence　laser　cutting　quality　In　this　paper,　the　influence　of　laser　head　movement　on　3D　laser　cutting　is　investigated.　Except　normal　movement　which　laser　head　is　vertical　to　work　piece　surface,　three　types　of　movement　defined　in　3D　laser　cutting　are　considered.　Experimental　design　method　is　used　to　analyse　cutting　result.　In　order　to　quantitatively　describe　the　relationship　between　cutting　quality　and　cutting　parameters,　artificial　neural　network(ANN)　has　been　setup.　The　quality　marks　system　is　used　to　evaluate　cutting　result.　The　test　shows　the　calculated　quality　points　by　ANN　is　very　similar　with　actual　cutting　result.　The　laser　head　forward　movement　is　better　than　the　others.　The　ANN　is　very　useful　to　optimize　cutting　parameters,　predict　cutting　result　and　deduce　new　information.