To　ease　the　singularity　of　within-class　scatter　matrix　due　to　the　small　sample　size　problem　for　linear　discriminant　analysis　(LDA)　method,　the　modified　2D　linear　discriminant　analysis　and　bi-directional　linear　discriminant　analysis　method　based　on　quaternion　matrix　were　proposed　to　recognize　a　color　face.　These　methods　made　full　use　of　the　information　of　the　spatial　distribution　of　color　images,　and　extracted　the　2DLDA　or　BDLDA　feature　by　reducing　the　dimensionality　in　both　column　and　row　directions,　and　smoothed　the　singularity　of　the　within-class　scatter　matrix.　By　using　the　FERET　color　face　database　and　AR　color　face　database,　experimental　results　show　that　this　approach　has　better　recognition　performance　than　the　2DPCA　or　BDPCA　method　based　on　quaternion　matrix.