To address the problem of dynamic performance fluctuations in the feed system of CNC machine tools due to load perturbation, which in turn affects machining accuracy, this paper proposes a load prediction and compensation strategy that combines digital twin technology with the dual-drive mechanism of a data model based on a two-axis feed system. First, a digital twin mechanism model of the CNC machine tool feeding system is constructed to simulate and compensate for the load perturbation and realize the virtual mapping of the actual system behavior. Subsequently, the recursive least squares method with a variable forgetting factor combined with the GRU-gated recurrent neural network method is used to dynamically correct and compensate for the mechanism model’s load prediction and compensation results. Finally, the dynamic updating of the experimental results at the visualization level and the interaction between reality and fiction is realized by building a digital twin experimental platform. The experimental results show that the method can control the relative prediction error within 4% and the relative compensation error within 6%, which can significantly improve the quality of workpiece surface machining and the overall performance of the machine tool.