Built　on　Weibull　cumulative　distribution　function　and　the　hysteresis　rule　of　Jiles–Atherton　model,　this　paper　proposes　a　new　hysteresis　function　suitable　for　modeling　the　hysteretic　characteristics.　After　the　domain　of　definition　expanded,　the　cumulative distribution　function　of　a　two-parameter　Weibull　distribution　is　employed　to　describe　the　skeleton　curve　of　the　hysteresis.　A　simplified　energy　conversion　equation　based　on　Jiles–Atherton　model　is　then　presented　to　describe　the　loop　curve.　The　proposed　hysteresis　model　is　solved　by　the　predictor–corrector　method.　From　calculation　results,　the　model　is　capable　of　providing　abundant　descriptions　of　hysteresis　and　approximating　some　hysteresis　with　low　deviations.　Parameter　determination　method　is　given　based　on　the　principle　of　minimizing　the　calculation　deviations　between　the　proposed　model　and　Jiles–Atherton　model.　Then　the　deviations　are　comprehensively　discussed　under　wider　value　range　when　the　magnetic　fields　are　not　lower　than　the　specified　values.　At　last,　the　parametric　analysis,　mainly　the　loop　parameters　on　hysteresis　curve,　maximum　value　and　loop　area,　is　completed.　With　simpler　expression　and　clearer　parameter　influence　compared　with　the　Jiles–Atherton　model,　the　model　is　suitable　for　modeling　various　types　of　hysteretic　systems,　especially　the　system　with　a　magnetic　hysteresis.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.　2024.