Average　neighborhood　margin　maximization　(ANMM)　is　a　local　supervised　metric　learning　approach,　which　aims　to　find　projection　directions　where　the　local　class　discriminability　is　maximized.　Furthermore,　it　has　no　assumption　of　class　distribution　and　works　well　on　small　sample　size.　In　this　work,　we　address　this　problem　in　the　quantum　setting　and　present　a　quantum　ANMM　algorithm　for　linear　feature　extraction.　More　specifically,　a　quantum　algorithm　is　designed　to　construct　scatterness　and　compactness　matrices　in　the　quantum　state　form.　Then　a　quantum　algorithm　is　presented　to　obtain　the　features　of　the　testing　sample　set　in　the　quantum　state　form.　The　time　complexity　analysis　of　the　quantum　ANMM　algorithm　shows　that　our　algorithm　may　achieve　an　exponential　speedup　on　the　dimension　of　the　sample　points　D,　and　a　quadratic　speedup　on　the　numbers　of　training　samples　N　and　testing　samples　M　compared　to　the　classical　counterpart　under　certain　conditions.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.