We　consider　the　Haldane　model,　a　two-band　model　in　monolayer　graphene　with　non-trivial　Chern　numbers.　Two　types　of　topological　defects,　monopoles　and　merons,　are　derived　from　the　model:　(a)　the　monopole　defects　occur　at　the　Dirac　points,　where　the　system　experiences　a　topological　transition　and　the　Chern　number　C　takes　an　indeterminate　value.　The　sign-change　of　the　mass　term　after　this　transition　indicates　different　topological　states　labeled　by　different　C　numbers;　(b)　the　meron　defects　occur　as　per　a　varying　mass　term　Summing　up　the　topological　charges　of　the　merons　leads　to　the　C　evaluation　for　the　energy　bands　of　an　insulating　bulk,　and　the　result　we　obtain　is　in　full　agreement　to　the　past　literature.　Furthermore,　in　this　paper　we　propose　a　high-C　model　through　studying　the　limitation　behavior　of　the　Hamiltonian　vector　in　the　neighborhood　of　the　topological　defects.　It　is　discovered　that　two　conducting　states　may　arise　form　the　edges,　where　the　lower　band　of　the　insulating　bulk　carries　a　higher　Chern　number,　C　=　+/-　2.