Accurate　prediction　of　the　magnetic　field　is　an　essential　guideline　for　permanent　magnetic　gear　design　and　optimization.　The　existing　magnetic　field　calculation　methods　are　divided　into　2-D　and　3-D　calculation　methods.　For　coaxial　magnetic　gears,　the　calculation　of　a　2-D　magnetic　field　can　be　employed　to　meet　the　design　requirements.　However,　as　a　new　spatial　transmission　mechanism,　nutation　magnetic　gear　relies　on　a　3-D　magnetic　field　to　transmit　force　and　torque.　Therefore,　the　2-D　magnetic　field　cannot　meet　the　design　requirements.　Hence,　it　is　necessary　to　accurately　predict　the　3-D　magnetic　field.　In　this　article,　an　analytical　mathematical　model　of　the　3-D　magnetic　field　of　magnetic　gears　is　established.　To　verify　the　accuracy　of　the　model,　the　magnetic　field　generated　by　the　same　magnetic　gear　is　predicted　by　the　proposed　model,　finite　element　method,　and　equivalent　current　method.　The　results　indicate　that　the　3-D　magnetic　field　mathematical　model　proposed　in　this　article　can　accurately　predict　a　3-D　magnetic　field,　which　is　an　essential　guide　for　the　research　and　optimization　of　magnetic　gears.