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To address the problem that traditional methods are difficult to reveal the sequence generation mechanism of dynamic error in machine tool multi-axis interpolation and the error time series features in each time dimension are interrelated, a cascaded dynamic error prediction model integrating chaotic representation (CR) and feature attention mechanism (FA) was proposed. Firstly, on the basis of proving that the time-varying evolution of multivariate dynamic error had chaotic characteristics, the phase space was reconstructed to represent the hidden information behind the time series of dynamic error parameters in the phase space. Then the fused feature attention mechanism further reshaped the dynamical state vector space of the original system by dynamically assigning phase point feature weights in the time dimension while reducing the redundancy of information in the high-dimensional evolution phase space. Finally, considering the long-range correlation of chaotic time-varying evolution, the bi-directional long short-term memory (Bi-LSTM) network model was used to approximate the dynamics in the chaotic phase space to achieve the effective prediction of dynamic error chaotic time series information. Compared with the Bi-LSTM model and the single cascade models CR-Bi-LSTM and FA-Bi-LSTM, the root mean square error of this algorithm was reduced by about 35%, 16% and 43%, respectively, as shown by the example of XK-L540 CNC milling machine with real data. The algorithm realized the phase space expression of dynamic error sequence generation mechanism in time dimension, and constantly played the main role of key phase point feature, with high prediction accuracy.