This　paper　dedicates　to　develop　a　systematic　approach　of　design　and　multi-dimensional　performance　optimization　of　the　Supercritical　carbon　dioxide　(SCO2)　compressor.　A　5　MW　SCO2　simple　regenerative　cycle　used　in　small　scale　lead-cooled　fast　reactor　(SLFR)　was　firstly　proposed　and　simulated　to　define　the　operation　condition　of　SCO2　compressor.　Under　the　inlet　and　outlet　condition　of　305.15　K/7.56　MPa　and　22　MPa,　isentropic　efficiency　and　mass　flow　rate　of　80%　and　69.88　kg·s−1　respectively　was　obtained.　Secondly,　a　single　stage　centrifugal　compressor　was　applied　as　the　SCO2　compressor　and　one-dimensional　(1D)　design　based　on　self-developed　code　was　conducted　to　determine　the　basic　geometry　of　the　compressor,　the　code　was　verified　with　experiments　and　shows　satisfactory　accuracy.　Additionally,　CFD　analysis　was　carried　out　to　validate　the　results　of　1D　design　and　also　shows　good　agreement.　Then,　three　one-dimensional　optimizations,　two　single　objective　optimizations　using　Particle　Swarm　Optimization　(PSO)　and　one　multi-objective　optimization　using　Genetic　Algorithm　(GA),　on　aerodynamic　efficiency　of　the　SCO2　centrifugal　compressor　were　performed　based　on　1D　design　code,　five　crucial　parameters　with　±　5%　variation　range　were　optimized.　The　1D　optimization　results　show　that　the　isentropic　efficiency　received　an　improvement　of　about　5　percentage　points　compared　to　that　of　1D　design.　Lastly,　three-dimensional　optimization　concentrated　on　the　blade　profile　of　impeller　were　conducted　on　a　fully　automatic　optimization　platform　to　further　improve　the　isentropic　efficiency　of　SCO2　centrifugal　compressor.　Wrap　angle　and　the　leading　and　trailing　edge　of　the　main　blade　were　optimized.　Two　optimal　impellers　with　wrap　angle　in　the　range　of　+　5%　and　−5%　were　obtained　respectively,　the　former　impeller　got　the　highest　pressure　ratio,　while　the　latter　one　gained　a　higher　isentropic　efficiency　but　the　lowest　pressure　ratio　over　the　whole　operation　range.　©　2021　Elsevier　Ltd