The　fractional　derivative　possesses　the　properties　of　describing　the　zero-order　differential　to　the　first-order　one　consecutively,　and　the　fractional　gradient　direction　of　the　curve　is　no　longer　perpendicular　to　its　tangent.　The　non-orthogonal　gradient　law　of　fractional　differential　can　be　used　to　describe　the　non-associated　flow　rules　between　the　plastic　flow　direction　and　the　yield　surface　of　soils.　Based　on　the　concept　of　characteristic　stress　and　the　critical　state　theory,　the　fractional-order　flow　law　is　used　to　describe　the　direction　of　plastic　strain　increment　of　soils　in　the　characteristic　stress　space,　and　the　fractional-order　critical　state　model　is　then　established.　The　fractional-order　differential　and　the　characteristic　stress　are　unified　by　using　the　established　constitutive　model　in　the　framework　of　the　critical　state　theory.　On　the　one　hand,　the　deformation　and　strength　properties　of　soils　under　triaxial　compression　and　extension　can　be　directly　described　by　the　established　constitutive　model.　On　the　other　hand,　the　method　for　determining　the　fractional　order　by　triaxial　tests　is　also　given.　There　are　only　5　material　parameters　with　clear　physical　meanings　in　the　established　constitutive　model,　and　they　can　be　easily　determined　by　the　conventional　triaxial　tests.　Moreover,　the　proposed　constitutive　model　can　also　be　simplified　into　the　modified　Cam-clay　model.　Finally,　the　new　model　is　validated　by　means　of　the　test　results　from　the　conventional　triaxial　tests.　©　2019,　Editorial　Office　of　Chinese　Journal　of　Geotechnical　Engineering.　All　right　reserved.