Thermal　error　of　ball　screws　seriously　affects　the　machining　precision　of　computerized　numerical　control　(CNC)　machine　tools　especially　in　high　speed　and　precision　machining.　Compensation　technology　is　one　of　the　most　effective　methods　to　address　the　thermal　issue,　and　the　effect　of　compensation　depends　on　the　accuracy　and　robustness　of　the　thermal　error　model.　Traditional　modeling　approaches　have　major　challenges　in　time　series　thermal　error　prediction.　In　this　paper,　a　novel　thermal　error　model　based　on　long　short-term　memory　(LSTM)　neural　network　and　particle　swarm　optimization　(PSO)　algorithm　is　proposed.　A　data-driven　model　based　on　LSTM　neural　network　is　established　according　to　the　time　series　collected　data.　The　hyperparameters　of　LSTM　neural　network　are　optimized　by　PSO,　and　then　a　PSO-LSTM　model　is　established　to　precisely　predict　the　thermal　error　of　ball　screws.　In　order　to　verify　the　effectiveness　and　robustness　of　the　proposed　model,　two　thermal　characteristic　experiments　based　on　step　and　random　speed　are　conducted　on　a　self-designed　test　bench.　The　results　show　that　the　PSO-LSTM　model　has　higher　accuracy　compared　with　the　radial　basis　function　(RBF)　model　and　back　propagation　(BP)　model　with　high　robustness.　The　proposed　method　can　be　implemented　to　predict　the　thermal　error　of　ball　screws　and　provide　a　foundation　for　thermal　error　compensation.