Gantry-type computer numerical control (CNC) machines are widely used in the manufacturing industry. A novel structure with moveable gantry is proposed to improve the traditional gantry-type machine structure’s disadvantage of taking up too much space. Geometric errors have direct impacts on the actual position of the tool, which significantly reduces the accuracy of machines. Errors of different components are always coupled and have uncertain effects on the total geometric error. Thus, it is essential to find an effective way to identify the dominant errors and do targeted compensation. First, a novel identification method using value leaded global sensitivity analysis (VLGSA) is proposed to find the dominant errors. In VLGSA, weighting factors which show the influence of the error range are used to modify the multi-body system (MBS) error model. Results show that the dominant errors in three directions respectively contribute 80%, 86% and 85% of the total error in their directions. Then, errors identified by VLGSA are modeled by least-square linear fitting and B-spline interpolation methods, respectively, according to the feature of error data. Finally, the models are applied in a new real-time compensation system developed on the Beckhoff TwinCAT servo system. Experimental results from the gantry-type CNC engraving and milling machine show the proposed method can help figure out the most dominant errors and reduce around 90% of the total error.