Federated　learning　(FL)　is　a　distributed　machine　learning　framework　that　enables　the　training　of　shared　models　without　the　need　to　share　local　data.　However,　FL　faces　challenges　in　heterogeneous　Internet　of　Things　(IoT)　environments,　including　communication　bottleneck,　staleness,　and　non-　independent　and　identically　distributed　(non-IID)　data.　To　tackle　these　challenges,　we　present　ASAFL,　an　Asynchronous　Federated　Learning　framework　with　an　Adaptive　Scheduling　Strategy.　Firstly,　we　quantify　the　potential　contribution　of　client　models　relative　to　the　server　model.　Secondly,　we　design　a　client　upload　strategy　to　reduce　the　uploading　of　redundant　models　with　low　contribution.　Finally,　we　propose　a　server　model　update　method　based　on　the　contributions　to　address　model　divergence　caused　by　staleness　and　non-IID　data.　Furthermore,　our　theoretical　analysis　guarantees　ASAFL＇s　convergence,　and　experiments　show　it　reduces　communication　overhead　by　over　70%　compared　to　traditional　asynchronous　FL.