Each　band,　which　is　the　image　of　the　same　object　on　different　frequency　bands　for　hyperspectral　image,　has　not　only　the　correlation　in　space,　but　also　a　strong　correlation　between　spectrum.　The　hyperspectral　image　compression　algorithms　need　to　consider　how　to　make　use　of　the　correlation　of　both　space　and　spectrum.　In　this　paper,　we　first　use　principal　component　analysis　(PCA)　to　remove　the　spectral　correlation.　Then　a　directional　lifting　wavelet　transform(DLWT)　is　used　to　remove　the　spatial　correlation.　The　experimental　results　show　that　the　proposed　image　compression　scheme　achieves　higher　performances　when　compared　with　DWT　based　Consultative　Committee　for　Space　Data　Systems(CCSDS).　©　2015　ACM.