In　this　paper,　a　new　compensation　method　of　thermal　error　is　proposed　based　on　Floyd　algorithm　and　homogeneous　transformation　matrices　(HTMs).　With　the　topological　structure　and　measured　data,　the　thermal　error　modelling　is　established.　Then,　according　to　the　improved　Floyd　minimum-distance　method　and　ant　colony　algorithm-based　back　propagation　neural　network　(ACO-BPN),　the　error　compensation　models　were　established　respectively.　A　comparison　between　the　Floyd　algorithm　compensation　method　and　a　typical　method　ACO-BPN　is　performed,　and　the　results　shows　that　the　Floyd　algorithm　has　advantages　of　higher　compensation　accuracy,　more　effective　and　shorter　time　than　ACO-BPN.　Under　variable　temperatures　conditions,　the　Floyd　compensation　method　also　has　higher　compensation　accuracy.