Artificial　designed　metamaterials　have　attracted　widespread　attention　because　of　its　unique　lattice　structure　and　special　physical　properties.　In　this　work,　a　chiral　auxetic　metamaterial　with　adjustable　band　gap　function　is　designed　based　on　the　shape　memory　polymer　(SMP)　with　special　thermomechanical　property.　Theory　and　finite　element　methods　are　used　to　investigate　the　relationship　between　the　elastic　modulus,　Poisson＇s　ratio　and　lattice　parameters　of　the　chiral　metamaterial.　Moreover,　the　dispersion　curves　of　the　metamaterial　under　different　strain　states　and　temperature　field　are　studied　by　finite　element　method.　The　evolution　processes　of　the　band　gap　with　the　variation　of　configuration　and　environmental　temperature　are　systematically　revealed.　The　results　show　that　the　elastic　modulus　can　be　tailored　by　adjusting　the　geometric　parameters　of　the　lattice,　and　the　Poisson＇s　ratio　is　-1.　The　band　gap　could　be　real-time　adjusted　by　external　stimuli　(mechanical　loadings,　temperature　field).　Based　on　the　relationship　between　the　geometric　parameters　and　the　band　gap,　the　required　properties　of　metamaterial　can　be　customized.　Moreover,　the　vibration　control　ability　of　the　metamaterial　can　be　further　optimized　by　adjusting　the　strain　of　metamaterial　and　the　temperature.　The　method　of　designing　metamaterials　with　tunable　and　programmable　mechanical　properties　and　acoustic　functions　provides　a　meaningful　reference　for　the　development　of　metamaterials　with　potential　applications.　©　2021