This　paper　provides　the　process　of　incremental　constitutive　integration　for　the　unified　hardening　model　combined　with　the　transformation　stress　method.　The　dimension-extending　technique　takes　the　hardening　function　of　the　hardening/softening　model　as　the　same　position　as　the　stress　components,　so　that　the　constitutive　integration　of　the　plasticity　can　be　reduced　to　an　initial　value　problem　of　differential-complementarity　equations,　which　is　solved　using　the　Gauss-Seidel　algorithm-based　Projection-Correction　for　the　mixed　complementarity　problem.　The　Gauss-Seidel　based　Projection-Correction　algorithm　does　not　require　the　calculation　of　the　Jacobean　matrix　of　the　potential　function,　making　it　relatively　easy　to　implement　in　programming.　The　unified　hardening　model　is　proposed　based　on　the　modified　Cam-Clay　model　and　the　sub-loading　surface　model,　and　the　elastic　properties　are　pressure-dependent.　Two　processing　methods,　backward　Euler　integration　and　exact　elastic　property,　are　used　for　the　variable　elasticity　properties.　The　constitutive　integration　of　the　increased　dimensional　unified　hardening　model　is　reduced　to　a　special　mixed　complementarity　problem　and　solved　by　the　proposed　algorithm,　which　does　not　need　to　calculate　the　Jacobean　matrix　of　the　potential　function,　and　greatly　simplifies　the　derivation　process.　Several　numerical　examples　are　given　to　verify　the　feasibility　of　the　incremental　constitutive　integration　in　the　unified　hardening　model,　including　the　single　integral　point　and　the　boundary　value　problems.　The　research　results　have　expanded　the　scope　of　use　of　the　Gauss-Seidel　based　Projection-Correction　algorithm.