Using　Faddeev-Senjanovic　path　integral　quantization　for　constrained　Hamilton　system,　we　quantize　SU(n)　N　=　2　supersymmetric　gauge　field　system　with　non-Abelian　Chern-Simons　topological　term　in　2　+　1　dimensions.　We　use　consistency　of　Coulomb　gauge　condition　to　naturally　deduce　a　new　gauge　condition.　Furthermore,　we　obtain　the　generating　functional　of　Green　function　in　phase　space,　deduce　the　angular　momentum　based　on　the　global　canonical　Noether　theorem　at　quantum　level,　obtain　the　fractional　spin　of　this　supersymmetric　system,　and　show　that　the　total　angular　momentum　is　the　sum　of　the　orbital　angular　momentum　and　spin　angular　momentum　of　the　non-Abelian　gauge　field.　Finally,　we　obtain　the　anomalous　fractional　spin　and　discover　that　the　fractional　spin　has　the　contributions　of　both　the　group　superscript　components　and　A(0)(s)(x)　charge.　(C)　2008　Elsevier　B.V.　All　rights　reserved.