Braking　torque　is　the　most　important　performance　parameter　for　a　permanent　magnet　retarder　used　in　heavy　vehicles.　This　paper　proposes　a　model　of　the　permanent　magnet　retarder　for　braking　torque　at　different　speeds　considering　the　skin　effect,　the　magnetic　leakage,　and　the　actual　path　of　the　eddy　currents.　Based　on　the　magnetic　equivalent　circuit　and　the　piecewise　function　method,　the　static　and　the　transient　air-gap　flux　density　models　are　established,　and　their　accuracy　is　verified　by　comparison　to　the　finite　element　method　(FEM).　The　permeability　distribution　curve　of　the　retarder　stator　is　obtained　by　a　simple　permeability-measuring　instrument,　considering　the　skin　effect　on　the　permeability　of　the　stator.　Thus,　the　effective　permeability　function　of　the　stator　is　obtained　at　different　rotational　speeds,　and　the　transient　air-gap　flux　density　model　is　optimized　using　the　effective　permeability　function.　The　simulation　results　showed　that　the　optimized　transient　air-gap　flux　density　of　the　calculation　model　was　in　good　agreement　with　the　FEM.　Finally,　the　calculation　model　of　the　eddy　current　braking　torque　was　verified　by　the　bench　test.