As　a　distributed　machine　learning　framework,　federated　learning　has　received　considerable　attention　in　recent　years　and　has　been　researched　and　applied　in　various　scenarios.　However,　the　system　heterogeneity　due　to　the　physical　characteristics　of　various　terminal　devices　has　led　to　the　straggler　effect,　making　the　practical　implementation　of　federated　learning　challenging.　Therefore,　we　propose　a　semi-asynchronous　federated　optimization　method　based　on　buffer　pre-aggregation.　This　method　allows　every　participant　to　engage　in　training　through　pre-aggregation　and　establishes　a　training　time　framework　based　on　the　pre-aggregation　time.　It　updates　the　model　adaptively　using　a　semi-asynchronous　communication　method　combined　with　lag　factors,　improving　communication　efficiency　while　maintaining　stable　accuracy.　Experimental　results　on　datasets　demonstrate　that　our　proposed　method　can　effectively　accelerate　the　training　process　of　federated　learning　compared　to　existing　federated　optimization　methods.　　©　2024　ACM.