Decentralized　storage　powered　by　blockchain　is　becoming　a　new　trend　that　allows　data　owners　to　outsource　their　data　to　remote　storage　resources　offered　by　various　storage　providers.　Unfortunately,　unqualified　storage　providers　easily　encounter　unpredictable　downtime　due　to　security　threats,　such　as　malicious　attacks　or　system　failures,　which　is　unacceptable　in　many　real-time　or　data-driven　applications.　As　a　result,　continuous　data　integrity　should　be　guaranteed　in　decentralized　storage,　which　ensures　that　data　is　intact　and　available　for　the　entire　storage　period.　However,　this　requires　frequent　checking　for　long　time　periods　and　incurs　heavy　burdens　of　both　communication　and　computation,　especially　in　a　big　data　scenario.　In　this　paper,　we　propose　an　efficient　continuous　big　data　integrity　checking　approach　for　decentralized　storage.　We　design　a　data-time　sampling　strategy　that　randomly　checks　the　integrity　of　multiple　files　at　each　time　slot　with　high　checking　probability.　Furthermore,　to　tackle　the　fairness　problem　derived　from　the　sampling　strategy,　we　propose　a　fair　approach　by　designing　an　arbitration　algorithm　with　the　verifiable　random　function.　Security　analysis　shows　the　security　of　our　approach　under　the　random　oracle　model.　Evaluation　and　experiments　demonstrate　that　our　approach　is　more　efficient　in　the　big　data　scenario　compared　with　the　state-of-the-arts.