This　paper　presents　a　topology　optimization　method　to　construct　adjustable　thermal　expansion　metamaterials.　The　negative　thermal　expansion　(NTE)　and　extreme　positive　thermal　expansion　(EPTE)　microstructures　are　designed,　respectively.　First,　the　effective　elastic　modulus　and　the　effective　thermal　expansion　coefficient　of　microstructure　are　derived　by　the　multiscale　asymptotic　homogenization　theory　based　on　the　periodic　characteristics　of　the　metamaterial.　Second,　a　topology　optimization　model　aiming　at　extreme　thermal　expansion　coefficient　is　established　and　solved　based　on　independent　continuous　topological　variables,　which　is　subjected　to　the　effective　elastic　modulus　and　structure　weight　fraction.　Then　a　cross-precision　progressive　optimization　method　is　provided　to　save　the　computation　time　and　make　a　smoother　boundary.　In　addition,　the　specific　topological　feature　for　the　initial　configuration　is　discussed.　Five　holes　are　the　necessary　condition　to　obtain　adjustable　thermal　expansion　metamaterials　for　four-axisymmetric　structures.　Finally,　a　transformation　strategy　from　NTE　to　EPTE　and　the　change　law　of　thermal　expansion　coefficient　bounds　with　effective　elastic　modulus　are　studied.　Numerical　examples　show　that　the　NTE　and　EPTE　can　be　designed　in　the　range　of　effective　elastic　modulus　from　0.01　to　0.05.　The　proposed　method　provides　a　reference　for　the　novel　configuration　design　of　metamaterials.