The　objective　of　this　paper　is　to　refine　the　calculation　method　for　improving　the　regression　accuracy　of　fatigue　failure　criterion　of　asphalt　binder　using　the　linear　amplitude　sweep　(LAS)　test,　especially　for　the　highly　modified　asphalt　binders.　The　maximum　stored　pseudo　strain　energy　(Max　W-R　s-based　failure　criterion　was　studied　for　interpreting　the　LAS　test　data　under　multiple-loading　rates　to　predict　the　fatigue　life　of　asphalt　binders.　However,　the　regression　accuracy　of　the　Max　WRs-based　failure　criterion　for　neat　asphalt　binders　is　generally　better　than　that　of　modified　binders.　In　this　paper,　a　parameter　of　total　released　pseudo　strain　energy　(TRPSE),　which　measures　the　area　under　the　pseudo　strain　energy　(PSE)　curve　until　fatigue　failure　occurs,　was　developed　as　a　material　characteristic　parameter,　which　demonstrates　that　no　matter　what　loading　rates　are　conducted　during　the　LAS　tests,　the　TRPSE　value　is　constant　at　a　specific　temperature　for　a　given　asphalt　binder.　The　proposed　TRPSE　value　was　obtained　from　the　averaged　results　of　the　six　replicates　under　three　LAS　loading　rates;　then　the　failure　criterion　was　recalculated,　and　the　regression　accuracy　significantly　improved　for　the　studied　neat　and　modified　binders.　Applying　this　improved　TRPSE-based　failure　criterion　for　the　prediction　of　fatigue　life　presented　more　reasonable　results,　especially　for　the　modified　binders　studied　at　multiple　temperatures　and　strain　amplitudes.