In　this　paper,　a　new　generalized　t　(new　Gt)　distribution　based　on　a　distribution　construction　approach　is　proposed　and　proved　to　be　suitable　for　fitting　both　the　data　with　high　kurtosis　and　heavy　tail.　The　main　innovation　of　this　article　consists　of　four　parts.　First　of　all,　the　main　characteristics　and　properties　of　this　new　distribution　are　outined.　Secondly,　we　derive　the　explicit　expression　for　the　moments　of　order　statistics　as　well　as　its　corresponding　variance-covariance　matrix.　Thirdly,　we　focus　on　the　parameter　estimation　of　this　new　Gt　distribution　and　introduce　several　estimation　methods,　such　as　a　modified　method　of　moments　(MMOM),　a　maximum　likelihood　estimation　(MLE)　using　the　EM　algorithm,　a　novel　iterative　algorithm　to　acquire　MLE,　and　improved　probability　weighted　moments　(IPWM).　Through　simulation　studies,　it　can　be　concluded　that　the　IPWM　estimation　performs　better　than　the　MLE　using　the　EM　algorithm　and　the　MMOM　in　general.　The　newly-proposed　iterative　algorithm　has　better　performance　than　the　EM　algorithm　when　the　sample　kurtosis　is　greater　than　2.7.　For　four　parameters　of　the　new　Gt　distribution,　a　profile　maximum　likelihood　approach　using　the　EM　algorithm　is　developed　to　deal　with　the　estimation　problem　and　obtain　acceptable.