TSVM　is　designed　to　solve　binary　classification　problems　with　less　computational　overhead　by　finding　two　hyperplanes　and　has　been　widely　used　to　solve　real-world　problems.　However,　in　real　scenarios,　the　data　used　for　learning　is　always　scattered　in　different　institutions　or　users.　At　the　same　time,　people　pay　more　attention　to　the　issue　of　personal　privacy　leakage.　Due　to　the　complex　privacy　protection　issues,　simply　collecting　all　the　data　for　model　training　is　no　longer　acceptable.　Federated　learning　has　recently　been　proposed　to　solve　this　problem.　It　completes　model　training　by　sharing　model　parameter　updates　in　the　form　of　data　that　remains　local.　But　there　is　still　no　algorithm　for　twin　support　vector　machines　under　the　framework　of　federated　learning.　Combining　the　characteristics　of　twin　support　vector　machine　and　federated　learning,　this　paper　proposes　a　federated　twin　support　vector　machine　algorithm　(FTSVM)　and　extends　the　twin　support　vector　machine　based　on　stochastic　gradient　descent　into　a　federated　support　vector　machine.　We　propose　a　unique　initialization　algorithm　and　integration　algorithm　to　ensure　the　accuracy　of　the　algorithm　and　the　effectiveness　of　privacy　protection.　Accuracy　experiments　are　carried　out　on　five　datasets,　and　the　accuracy　is　basically　the　same　as　that　of　the　TSVM　based　on　gradient　descent.　Ablation　experiments　show　that　as　the　number　of　participants　increases,　the　accuracy　of　the　FTSVM　is　significantly　higher　than　the　average　accuracy　of　the　Stand-alone　TSVM.　Time　experiments　show　that　the　time　overhead　of　FTSVM　increases　linearly　with　the　number　of　participants.　These　experiments　demonstrate　the　accuracy,　effectiveness,　and　possibility　of　application　in　real-world　scenarios　of　our　proposed　FTSVM.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.