Objective:　Diabetic　retinopathy　(DR)　is　one　of　the　leading　causes　of　vision　loss　and　early　diagnosis　is　crucial　to　prevent　blindness.　Diagnosing　DR　is　time-consuming　and　labor-intensive,　resulting　in　a　high　risk　of　misdiagnosis　within　resource-constrained　clinical　environment.　Automated　diagnostic　models　offer　promising　solutions　for　rapid　DR　identification,　precise　severity　stratification,　and　streamlined　reporting　timelines.　However,　the　clinical　application　may　be　significantly　constrained　when　deal　with　data　that　is　cross-center,　cross-population,　or　class-imbalanced.　Methods:　We　propose　the　Grade-Skewed　Domain　Adaptation　Network　with　Coordinate　and　Category　Attention　(G2C-Net)　model,　which　integrates　domain　adaptation,　spatial　channel　attention　mechanisms,　and　category　attention　to　improve　the　diagnostic　accuracy　in　cross-center,　cross-population　and　Grade-Skewed　(GS)　situations.　The　G2C-Net　model　is　trained　and　tested　using　two　large　datasets　of　retinal　images　graded　for　various　stages　of　DR.　The　performance　is　evaluated　in　precision,　sensitivity,　F1-score,　specificity,　and　accuracy　metrics　for　each　grade　of　DR　images　on　both　the　source　and　target　domains.　Results:　By　comparing　performance　of　DR　grading　among　different　models,　the　G2C-Net　model　achieves　the　best　evaluation　metrics　on　both　the　source　domain　and　the　target　domain.　Specifically,　the　G2C-Net　model　improves　precision,　sensitivity,　F1-score,　specificity　and　accuracy　for　DR　grading　by　23.7%,　21.1%,　24.3%,　6.0%,　and　7.5%　respectively　on　the　source　domain,　and　37.9%,　30.7%,　31.1%,　11.9%,　and　6.1%　respectively　on　the　target　domain.　Conclusion:　The　G2C-Net　model　significantly　reduces　class-imbalance-induced　grading　errors,　addresses　cross-domain　distribution　shifts　in　clinical　data,　and　achieves　superior　performance　in　early　diagnosis　of　DR.