Utilizing　multiple　modalities　to　learn　a　good　distance　metric　is　of　vital　importance　for　various　clinical　applications.　However,　it　is　common　that　modalities　are　incomplete　for　some　patients　due　to　various　technical　and　practical　reasons　in　healthcare　datasets.　Existing　metric　learning　methods　cannot　directly　learn　the　distance　metric　on　such　data　with　missing　modalities.　Nevertheless,　the　incomplete　data　contains　valuable　information　to　characterize　patient　similarity　and　modality　relationships,　and　they　should　not　be　ignored　during　the　learning　process.　To　tackle　the　aforementioned　challenges,　we　propose　a　metric　learning　framework　to　perform　missing　modality　completion　and　multi-modal　metric　learning　simultaneously.　Employing　the　generative　adversarial　networks,　we　incorporate　both　complete　and　incomplete　data　to　learn　the　mapping　relationship　between　modalities.　After　completing　the　missing　modalities,　we　use　the　nonlinear　representations　extracted　by　the　discriminator　to　learn　the　distance　metric　among　patients.　Through　jointly　training　the　adversarial　generation　part　and　metric　learning,　the　similarity　among　patients　can　be　learned　on　data　with　missing　modalities.　Experimental　results　show　that　the　proposed　framework　learns　more　accurate　distance　metric　on　real-world　healthcare　datasets　with　incomplete　modalities,　comparing　with　the　state-ofthe-art　approaches.　Meanwhile,　the　quality　of　the　generated　modalities　can　be　preserved.