A　clinically　meaningful　distance　metric,　which　is　learned　from　measuring　patient　similarity,　plays　an　important　role　in　clinical　decision　support　applications.　Several　metric　learning　approaches　have　been　proposed　to　measure　patient　similarity,　but　they　are　mostly　designed　for　learning　the　metric　at　only　one　time　point/interval.　It　leads　to　a　problem　that　those　approaches　cannot　reflect　the　similarity　variations　among　patients　with　the　progression　of　diseases.　In　order　to　capture　similarity　information　from　multiple　future　time　points　simultaneously,　we　formulate　a　multi-task　metric　learning　approach　to　identify　patient　similarity.　However,　it　is　challenging　to　directly　apply　traditional　multi-task　metric　learning　methods　to　learn　such　similarities　due　to　the　high　dimensional,　complex　and　noisy　nature　of　healthcare　data.　Besides,　the　disease　labels　often　have　clinical　relationships,　which　should　not　be　treated　as　independent.　Unfortunately,　traditional　formulation　of　the　loss　function　ignores　the　degree　of　labels＇　similarity.　To　tackle　the　aforementioned　challenges,　we　propose　mtTSML,　a　multi-task　triplet　constrained　sparse　metric　learning　method,　to　monitor　the　similarity　progression　of　patient　pairs.　In　the　proposed　model,　the　distance　for　each　task　can　be　regarded　as　the　combination　of　a　common　part　and　a　task-specific　one　in　the　transformed　low-rank　space.　We　then　perform　sparse　feature　selection　for　each　individual　task　to　select　the　most　discriminative　information.　Moreover,　we　use　triplet　constraints　to　guarantee　the　margin　between　similar　and　less　similar　pairs　according　to　the　ordered　information　of　disease　severity　levels　(i.e.　labels).　The　experimental　results　on　two　real-world　healthcare　datasets　show　that　the　proposed　multi-task　metric　learning　method　significantly　outperforms　the　state-of-theart　baselines,　including　both　single-task　and　multi-task　metric　learning　methods.