The moving components and servo control systems of computer numerical control (CNC) machine tools spent a substantial energy but received less attention regarding energy saving. This article presents a novel energy saving methodology of feed system using a data-model hybrid driven design optimization approach for the integrated design of moving component structural geometry and control system. Surrogate models are built based on the design of experimental data to avoid time-consuming finite element analysis. The energy consumption mechanism model is constructed via energy flow analysis method. The data-model hybrid modeling method realizes the collaborative optimization of the machine tool feed system structure and controller, while simultaneously accelerating the optimization process. A multi-objective trade-off model with energy consumption and deformation is established. Three different multi-objective optimization approaches are taken to drive the developed multi-objective optimization model. The control performance of the feed system is demonstrated through simulation analysis. Results indicate that the optimized scheme can reduce energy consumption by over 10% and maximum deformation of the tool holder by over 14%. Note to Practitioners—This article is motivated by the problem that a significant energy consumption occurs when the CNC machine tool feed system continuously drives the moving components to move, accelerate or decelerate. The previous studies to cope with this problem broadly are to separately analyze energy-saving characteristics of the structure or control system of the CNC machine tool feed system. This article suggests a novel data-model hybrid approach for energy saving of machine tool feed system, which simultaneously integrates design of moving component structural geometry and servo control system. In this article, we mathematically derive an energy consumption mechanism model of the CNC machine tool feed system. By using surrogate assisted method, a multi-objective trade-off model with energy consumption and deformation is established. Simulation experiments indicate that this approach is feasible and can significantly reduce the energy consumption of CNC machine tool feed system.