In　this　paper　a　gauge　theory　is　proposed　for　the　two-band　model　of　Chern　insulators.　Based　on　the　so-called＇t　Hooft　monopole　model,　a　U(1)　Maxwell　electromagnetic　sub-field　is　constructed　from　an　SU(2)　gauge　field,　from　which　arise　two　types　of　topological　defects,　monopoles　and　merons.　We　focus　on　the　topological　number　in　the　Hall　conductance　sigma(xy)=e(2)/hC,　where　C　is　the　Chern　number.　It　is　discovered　that　in　the　monopole　case　C　is　indeterminate,　while　in　the　meron　case　C　takes　different　values,　due　to　a　varying　on-site　energy　m.　As　a　typical　example,　we　apply　this　method　to　the　square　lattice　and　compute　the　winding　numbers　(topological　charges)　of　the　defects;　the　C-evaluations　we　obtain　reproduce　the　results　of　the　usual　literature.　Furthermore,　based　on　the　gauge　theory　we　propose　a　new　model　to　obtain　the　high　Chern　numbers　vertical　bar　C　vertical　bar　=　2,　4.