The　morphotropic　phase　boundary　(MPB),　which　is　the　boundary　separating　a　tetragonal　phase　from　a　rhombohedral　phase　by　varying　the　composition　or　mechanical　pressure　in　ferroelectrics,　has　been　studied　extensively　for　decades　because　it　can　lead　to　strong　enhancement　of　piezoelectricity.　Recently,　a　parallel　ferromagnetic　MPB　was　experimentally　reported　in　the　TbCo2-DyCo2　ferromagnetic　system　and　this　discovery　proposes　a　new　way　to　develop　potential　materials　with　giant　magnetostriction.　However,　the　role　of　magnetic　domain　switching　and　spin　reorientation　near　the　MPB　region　is　still　unclear.　For　the　first　time,　we　combine　micromagnetic　theory　with　Monte　Carlo　simulation　to　investigate　the　evolution　of　magnetic　domain　structures　and　the　corresponding　magnetization　properties　near　the　MPB　region.　It　is　demonstrated　that　the　magnetic　domain　structure　and　the　corresponding　magnetization　properties　are　determined　by　the　interplay　among　anisotropy　energy,　magnetostatic　energy　and　exchange　energy.　If　the　anisotropy　energy　barrier　is　large　compared　with　the　magnetostatic　energy　barrier　and　the　exchange　energy　barrier,　the　MPB　region　is　a　T　and　R　mixed　structure　and　magnetic　domain　switching　is　the　dominant　mechanism.　If　the　anisotropy　energy　barrier　is　small,　the　MPB　region　will　also　contain　M　phases　and　spin　reorientation　is　the　dominant　mechanism.　Our　work　could　provide　a　guide　for　the　design　of　advanced　ferromagnetic　materials　with　enhanced　magnetostriction.