In　some　cases　in　order　to　avoid　interference　during　3D　laser　cutting　of　thin　metal　laser　head　could　not　be　kept　vertical　to　the　surface　of　a　work　piece.　In　such　situations　the　cutting　quality　depends　on　not　only　＂typical＂　cutting　parameters　but　also　on　the　slant　angle　of　the　laser　head.　Traditionally,　many　tests　had　to　be　done　in　order　to　obtain　best　cutting　results.　In　this　paper　an　experimental　design　is　employed　to　reduce　the　number　of　tests　and　collect　experimental　training　and　test　sets.　An　artificial　neural　network　(ANN)　approach　has　been　developed　to　describe　quantitatively　the　relationship　between　cutting　quality　and　cutting　parameters　in　the　non-vertical　laser　cutting　situation.　A　quality　point　system　is　used　to　evaluate　the　cutting　result　of　thin　sheet　quantitatively.　The　construction　of　network　is　also　investigated.　Testing　of　this　novel　method　shows　that　the　calculated　＂quality　point＂　using　ANN　is　quite　closely　in　accord　with　the　actual　cutting　result.　The　ANN　is　very　successful　for　optimizing　parameters,　predicting　cutting　results　and　deducing　new　cutting　information.