The　dramatically　increased　wireless　communication　needs　make　non-renewable　spectrum　resources　extremely　scarce　and　costly.　Consortium　blockchain　realizes　trusted　spectrum　sharing　among　untrusted　spectrum　owners.　Yet,　most　existing　studies　ignore　spectrum　sharing　among　blockchains,　which　greatly　reduce　spectrum　utilization.　In　the　paper,　we　focus　on　cross-chain　spectrum　sharing.　We　propose　a　Fine-grained　Cross-chain　Spectrum　Sharing　mechanism　based　on　Oracle　(FCSSO)　to　realize　trusted　and　efficient　cross-chain　spectrum　transactions.　To　guarantee　benefits　of　spectrum　owners,　we　design　a　fine-grained　time　partition　method　to　decide　spectrum　renting　time　in　transactions.　The　method　reduces　the　waste　of　owners＇　available　spectrum　time　caused　by　spectrum　handoff.　Extensive　simulation　proves　the　positive　impact　of　the　proposed　fine-grained　time　partition　method,　and　FCSSO　outperforms　two　representative　cross-chain　mechanisms　from　two　aspects:　spectrum　owners＇　benefits　and　spectrum　utilization.