Topology　optimization　is　one　of　the　most　common　methods　for　design　of　material　distribution　in　mechanical　metamaterials,　but　resulting　in　expensive　computational　cost　due　to　iterative　simulation　of　finite　element　method.　In　this　work,　a　novel　deep　learning-based　topology　optimization　method　is　proposed　to　design　mechanical　microstructure　efficiently　for　metamaterials　with　extreme　material　properties,　such　as　maximum　bulk　modulus,　maximum　shear　modulus,　or　negative　Poisson’s　ratio.　Large　numbers　of　microstructures　with　various　configurations　are　first　simulated　by　modified　solid　isotropic　material　with　penalization　(SIMP),　to　construct　the　microstructure　data　set.　Subsequently,　the　ResUNet　involved　generative　and　adversarial　network　(ResUNet-GAN)　is　developed　for　high-dimensional　mapping　between　optimization　parameters　and　corresponding　microstructures　to　improve　the　design　accuracy　of　ResUNet.　By　given　optimization　parameters,　the　well-trained　ResUNet-GAN　is　successfully　applied　to　the　microstructure　design　of　metamaterials　with　different　optimization　objectives　under　proper　configurations.　According　to　the　simulation　results,　the　proposed　ResUNet-GAN-based　topology　optimization　not　only　significantly　reduces　the　computational　duration　for　the　optimization　process,　but　also　improves　the　structure　precise　and　mechanical　performance.　©　The　Author(s)　2024.