As　many　countries　have　promulgated　laws　on　the　protection　of　user　data　privacy,　how　to　legally　use　user　data　has　become　a　hot　topic.　With　the　emergence　of　collaborative　learning,　also　known　as　federated　learning,　multiple　participants　can　create　a　common,　robust,　and　secure　machine　learning　model　aimed　at　addressing　such　critical　issues　of　data　sharing　as　privacy,　security,　and　access,　etc.　Unfortunately,　existing　research　shows　that　collaborative　learning　is　not　as　secure　as　it　claims,　and　the　gradient　leakage　is　still　a　key　problem.　To　deal　with　this　problem,　a　collaborative　learning　solution　based　on　chained　secure　multi-party　computing　has　been　proposed　recently.　However,　there　are　two　security　issues　in　this　scheme　that　remain　unsolved.　First,　if　semi-honest　users　collude,　the　honest　users＇　gradient　also　leaks.　Second,　if　one　of　the　users　fails,　it　also　cannot　guarantee　the　correctness　of　the　aggregation　results.　In　this　paper,　we　propose　a　privacy-preserving　and　verifiable　chain　collaborative　learning　scheme　to　solve　this　problem.　First,　we　design　a　gradient　encryption　method,　which　can　solve　the　problem　of　gradient　leakage.　Second,　we　create　a　verifiable　method　based　on　homomorphic　hash　technology.　This　method　can　ensure　the　correctness　of　users＇　aggregation　results.　At　the　same　time,　it　can　also　track　users　who　aggregate　wrong.　Compared　with　other　solutions,　our　scheme　is　more　efficient.　©　2021　IEEE.