Blockchain　has　emerged　as　a　decentralized　platform　for　e-voting.　Among　various　blockchain-based　voting　systems,　score　voting　provides　flexible　choices　and　better　reflects　public　opinions.　However,　existing　blockchain-based　score　voting　systems　suffer　from　heavy　range　proof　overheads,　and　are　much　inefficient　compared　with　other　blockchain-based　voting　systems.　Besides,　voter　anonymity　in　these　systems　is　not　rigorously　addressed.　In　this　paper,　we　propose　an　efficient,　flexible　and　privacy-preserving　score　voting　system,　named　ACB-Vote,　from　anonymously　convertible　ballots.　ACB-Vote　achieves　voting　anonymity　with　BBS+　signature　and　signature　of　knowledge.　Driven　by　convertibly　linkable　signatures　(CLS),　ACB-Vote　allows　cast　ballots　to　be　converted,　where　the　conversion　mechanism　prevents　anonymous　voters　from　multiple　voting.　Besides,　the　proposed　system　avoids　heavy　range　proofs,　enables　batch　ballot　verification　and　facilitates　flexible　tallying　methods.　We　formally　define　a　security　model　for　ACB-Vote　and　provide　rigorous　security　proofs.　Experiments　show　that　the　efficiency　of　ACB-Vote　is　competitive　compared　with　the　previous　score　voting　systems　and　is　affordable　in　blockchain　environments.