A　fractional　viscoelastic　kernel　function　is　proposed　to　describe　the　modulus　evolution　during　the　creep　and　stress　relaxation　behavior　of　quasi-brittle　materials.　A　unified　fractional　viscoelastic　model　for　creep　and　stress　relaxation　is　further　developed,　which　has　the　advantages　of　few　parameters　and　high　accuracy.　The　model　can　be　degenerated　into　the　basic　viscoelastic　models　under　different　values　of　fractional　order.　The　relationship　between　the　force　state　in　non-ordinary　state-based　peridynamics　and　the　stress　tensor　in　the　continuum　mechanics　constitutive　model　is　established.　The　developed　fractional　viscoelastic　model　is　then　integrated　into　the　peridynamic　framework　to　create　a　unified　creep　and　stress　relaxation　peridynamic　method.　The　calibration　method　of　the　model　parameters　is　also　determined　through　the　equivalence　of　the　peridynamics　and　the　continuum　mechanics,　and　the　influence　rules　of　parameters　on　the　viscoelastic　behavior　of　materials　are　discussed.　The　effectiveness　of　the　proposed　peridynamic　method　is　verified　by　numerical　simulations　of　a　plate,　bar,　slate,　and　beam.　The　proposed　method　can　accurately　describe　the　deformation　process　from　continuous　to　discontinuous　in　creep　and　stress　relaxation.　This　study　provides　a　valuable　numerical　tool　for　simulating　structural　damage　caused　by　creep　and　stress　relaxation　in　engineering　structures　during　long-term　operation.　©　2024