In　some　cases,　in　order　to　avoid　interference　during　3D　laser　cutting　of　thin　metal　a　laser　head　could　not　be　kept　vertical　to　the　surface　of　a　work　piece.　In　such　situations,　the　cutting　quality　depends　not　only　on　＂typical＂　cutting　parameters　but　also　on　the　slant　angle　of　the　laser　head.　Traditionally,　many　tests　had　to　be　done　in　order　to　obtain　the　best　cutting　results.　In　this　paper,　an　experimental　design　is　employed　to　reduce　the　number　of　tests　and　an　artificial　neural　network　(　ANN)　is　set　up　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　the　thin　sheet　quantitatively.　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.