Prediction models based on deep learning often suffer from “catastrophic forgetting” caused by the inability to adapt to new degraded data. This is currently a hot and difficult topic in the field of artificial intelligence research, and also one of the constraints on the development of intelligent equipment. The accuracy evolution process of CNC machine tools has chaotic characteristics. Therefore, a chaotic self-evolution prediction method for the motion accuracy of CNC machine tools based on chaos theory and incremental learning is proposed. Firstly, it has been proven that the dynamic variation of motion errors in CNC machine tools is a chaotic evolution process of a complex nonlinear dynamic system. It is proposed to reconstruct the evolution trajectory of the precision system in the chaotic phase space through phase space reconstruction. Then, a motion accuracy chaotic evolution model based on deep long short-term memory (LSTM) network is established, utilizing the LSTM network's excellent ability to accurately capture long-term dependencies of time series, to track the inherent laws of the evolution trajectory of CNC machine tool motion accuracy in chaotic phase space. Finally, a learning without forgetting incremental learning method is proposed in the chaotic evolution model to establish a motion accuracy chaotic self-evolution prediction model. This model uses joint optimization and knowledge distillation methods to update parameters, allowing the model to adapt to new degraded data while also conveying the soft objectives of old tasks. It solves the problem of “catastrophic forgetting” during dataset updates, improving the accuracy and robustness of long-term predictions. The experiment shows that the evaluation indicators MSE,MAE and MAPE predicted by the method proposed have decreased in fluctuation amplitude by 70.56%, 33.31%, and 35.77%, respectively, compared to the non-LwF module. This proves the accuracy of the proposed prediction method. Further module ablation experiments also verify that the method proposed is superior to traditional methods in terms of prediction accuracy and robustness.