Outsourcing　storage　has　emerged　as　an　effective　solution　to　manage　the　increasing　volume　of　data.　With　the　popularity　of　pay-as-you-go　payment　models　in　outsourcing　storage,　data　auditing　schemes　that　prioritize　timeliness　can　be　valuable　evidence　for　elastic　bill　settlement.　Unfortunately,　existing　data　auditing　schemes　do　not　sufficiently　consider　timeliness　during　auditing.　Furthermore,　practical　data　auditing　schemes　should　have　the　capability　to　check　the　integrity　of　scalable　data.　In　this　paper,　we　propose　a　blockchain-based　dynamic　data　auditing　scheme　with　strong　timeliness　to　ensure　that　data　stored　in　outsourcing　storage　systems　remain　intact.　Our　scheme　encapsulates　timestamps　into　homomorphic　verifiable　tags　to　simultaneously　check　data　integrity　and　timestamp　validity.　To　achieve　dynamicity,　we　utilize　the　Merkle　hash　tree　to　store　the　tags,　allowing　for　block-level　dynamic　operations.　Additionally,　by　leveraging　the　transparency,　non-repudiation,　and　tamper　resistance　of　blockchain　technology,　we　design　a　blockchain-based　data　auditing　framework　to　prevent　malicious　behavior　from　all　entities.　We　then　formally　prove　the　soundness　and　privacy　of　our　scheme.　Finally,　we　conduct　theoretical　analysis　and　experimental　evaluation　to　demonstrate　that　the　performance　of　our　scheme　is　of　acceptable　efficiency　to　existing　works　in　terms　of　computation　cost,　communication　overhead,　and　storage　overhead.