Federated　Learning　(FL)　is　a　distributed　machine　learning　system　designed　to　effectively　address　potential　data　privacy　concerns,　making　it　particularly　promising　for　the　Internet　of　Things　(IoT).　However,　challenges　arise　due　to　the　trust　and　heterogeneity　of　IoT　devices.　FL　often　assumes　devices　are　trustworthy　and　curious,　which　is　impractical　in　the　realistic　IoT　environment　where　the　trustworthiness　of　participating　devices　becomes　an　intractable　problem.　Additionally,　the　diverse　computational　power　and　communication　efficiency　across　IoT　devices　impact　the　efficiency　and　performance　of　FL.　To　address　these　challenges　and　enable　the　effective　implementation　of　FL　in　the　IoT　environment,　this　article　proposes　a　Trusted　Hierarchical　Asynchronous　Federated　Learning　Framework　(T-FedHA).　The　framework　introduces　a　“Device-Edge-Central”　hierarchy　and　employs　a　distributed　trust　management　model.　This　model　manages　the　trust　of　IoT　devices,　selecting　devices　that　meet　trust　requirements　for　FL　training.　This　enhances　the　security　and　trustworthiness　of　the　overall　FL　system.　Furthermore,　T-FedHA　integrates　standard　FL　methods　with　a　hierarchical　asynchronous　strategy　that　includes　edge　servers.　This　approach　improves　model　aggregation　and　update　processes,　employing　an　asynchronous　technique　that　considers　the　staleness　of　model　updates　to　enhance　overall　performance　and　effectiveness.　Extensive　experiments　confirm　the　efficacy　of　T-FedHA.　The　distributed　trust　management　model　efficiently　calculates　and　manages　IoT　device　trust,　allowing　only　trusted　devices　to　participate　in　FL　training.　The　hierarchical　asynchronous　approach　proves　more　feasible　and　efficient,　as　well　as　robust　and　flexible,　contributing　to　the　reliability　of　the　proposed　framework.　©　2023　Elsevier　Ltd