Edge　anomaly　detection　guarantees　the　security　of　Internet-of-Things　(IoT).　The　emerging　Federated　Learning　(FL)　can　ameliorate　the　privacy-leakage　and　data-island　issues　in　edge　anomaly　detection.　However,　existing　FL-based　solutions　still　reveal　limitations　in　handling　statistical　and　system　heterogeneity,　thus　they　cannot　adapt　to　anomaly　detection　in　complex　edge　environments.　To　address　these　problems,　we　propose　FedGPA,　a　novel　Federated　learning　with　Global-Personalized　collaboration　for　edge　Anomaly　detection.　First,　we　design　a　conditional　calculation　component　to　transform　traffic　features　into　global　and　personalized　feature　vectors.　Next,　we　introduce　contrast　and　magnitude　losses　in　the　global-class　embedding　module　and　guide　the　learning　of　global　feature　vectors　with　the　embedding　of　sample　classes.　Then,　we　adopt　cross-entropy　loss　to　guide　the　learning　of　personalized　feature　vectors.　Finally,　the　cosine　similarity　between　the　updated　gradients　of　cross-entropy　and　overall　losses　is　used　to　determine　the　loss　replacement,　thereby　accelerating　the　model　training.　Notably,　we　prove　the　FedGPA　can　converge　stably　during　the　aggregation　process.　Using　real-world　testbed　and　traffic　datasets,　extensive　experiments　verify　the　effectiveness　of　the　FedGPA,　which　efficiently　solves　statistical　and　system　heterogeneity.　Compared　to　state-of-the-art　methods,　the　FedGPA　achieves　higher　detection　accuracy　and　shorter　training　time,　exhibiting　better　scalability　and　convergence.