The　hysteresis　model　has　long　been　widely　discussed　to　describe　the　dynamic　behavior　of　magnetic　materials　or　devices.　Most　models　solve　the　hysteresis　with　the　completely　absent　or　present　phase　lags　of　the　critical　points　at　various　frequencies.　However,　the　variation　of　the　hysteresis　loop　with　the　frequency　is　not　effectively　demonstrated　as　the　measurement　shows　that　the　phase　lags　are　changing　with　the　frequency.　This　is　assumed　to　be　caused　by　neglecting　the　connection　between　the　loop　and　time-domain　curve,　which　is　necessary　to　determine　the　form　of　the　time-dependent　loss.　Jiles-Atherton　model　is　taken　here　as　an　example　and　the　connections　under　different　frequencies　are　revealed　from　analyzing　the　model　errors.　According　to　the　test　data　of　the　Terfenol-D　material,　a　new　methodology　is　proposed　to　consider　the　influence　of　the　frequency-dependent　loss　on　the　hysteresis　loop.　The　methodology　idea　is　derived　from　the　viewpoint　of　phase　lag　and　amplitude　attenuation　of　the　magnetization　caused　by　the　loss.　Meanwhile,　the　equation　is　established　built　on　the　viscoelastic　damping　assumption　to　naturally　realize　the　phase　lag　of　all　the　points.　From　the　qualitative　analysis,　the　proposed　model　removes　the　limitations　in　computing　the　loop　widths　and　phase　lags　at　different　frequencies.　Furthermore,　the　model　is　validated　as　it　corresponds　well　with　the　experimental　results.　With　strong　description　ability,　clear　parametric　influence　and　simple　expression,　the　proposed　model　may　become　a　substitute　for　classic　frequency-dependent　hysteresis　models.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.　2024.