A　non-Gaussian　model　is　developed　to　precisely　describe　the　chemo-mechanical　coupled　large　deformation　of　responsive　hydrogels.　In　this　model,　the　free-energy　density　is　composed　of　two　parts,　including　the　elastic　energy　due　to　stretching　of　cross-linked　polymer　networks　described　by　Gent　hyperelastic　model,　and　the　mixture　energy　of　polymer　network　and　described　by　Flory-Huggins　theory.　The　effects　of　junction　functionality　and　chain　entanglements　are　investigated　by　analyzing　free　swelling　of　a　cubic　hydrogel　and　constrained　swelling　of　a　blanket　layer　of　the　gel.　The　present　model　is　found　to　exhibit　obvious　hardening　characteristic　during　large　deformation　of　the　hydrogel,　and　the　considerations　of　functionality　of　junctions　and　chain　entanglements　are　essential　in　the　coupled　chemo-mechanical　deformation　analysis　of　hydrogels.