The　governing　equation　of　the　original　peridynamics　is　derived　from　the　energy　equation　of　work　done　by　conservative　forces,　which　cannot　reasonably　reflect　the　viscoelastic　deformation　behavior　of　materials　and　the　energy　dissipation　of　the　system.　To　solve　this　problem,　a　peridynamics　method　considering　the　work　done　by　non-conservative　forces　is　proposed.　The　theoretical　framework　includes　two　parts:　viscoelastic　interaction　of　material　points　and　its　motion　equation,　and　rate　dependent　fracture　criterion　of　bond.　In　describing　the　movement　of　material　points,　based　on　the　understanding　of　the　deformation　mechanism　of　concrete,　the　viscoelastic　interaction　model　between　material　points　is　proposed.　The　viscoelastic　motion　equation　is　established　by　using　the　Hamilton’s　principle　considering　energy　dissipation.　Using　the　viscoelastic　peridynamics　method　and　the　energy　density　equivalent　method　of　continuum　mechanics,　the　determination　methods　of　elastic　parameters　and　viscous　parameters　are　proposed.　In　terms　of　describing　bond　fracture　and　material　strength,　the　rate　dependent　fracture　criterion　of　bond　is　developed　by　using　the　dynamic　uniaxial　S　criterion　of　concrete.　Numerical　experiments　are　conducted　to　investigate　the　functions　and　advantages　of　the　viscoelastic　peridynamics　method　proposed.　The　results　show　that　the　peridynamics　method　proposed　can　reasonably　reflect　the　influence　of　loading　rate　on　the　deformation,　strength,　and　cracking　behavior　of　concrete.　©　2022　Science　Press.　All　rights　reserved.