In　the　field　of　precision　manufacturing,　error　compensation　of　parts　is　the　key　to　improve　product　quality　and　manufacturing　efficiency.　This　paper　presents　a　Long　Short-Term　Memory　Network　(LSTM)　model　based　on　the　Gray　Wolf　optimization　algorithm　designed　to　optimize　part　error　compensation.　First,　we　introduce　the　sources　of　part　errors　and　their　impact　on　the　manufacturing　process.　Then,　we　elaborate　the　application　of　LSTM　network　in　predicting　and　compensating　part　errors　by　selecting　appropriate　features　through　correlation　analysis.　Through　experiments,　we　verify　the　effectiveness　of　the　Gray　Wolf　optimization-based　LSTM　model　in　part　error　prediction　and　compensation.　The　experimental　results　show　that　compared　with　the　traditional　method,　the　model　in　this　paper　has　a　significant　improvement　in　both　error　prediction　accuracy　and　compensation　efficiency.