The thermal error from a dual direct feed axis driven by linear motors was analyzed and the error compensation method was proposed to improve the accuracy of the system movement. The causes of thermal error generation in the motion processes and the complexity of the compensation were discussed. And then a compensation method based on Latent Variable Regression(LVR) was applied to improvement of the positioning accuracy of the feeding axis. With the method, a laser interferometer was utilized to obtain the thermal deformation of the feed axis in real-time. Some thermocouples and infrared thermometers were used to measure the temperatures of some key points at the linear axis. A regression model based on latent variable model was established to recognize the thermal deformation behavior of the mechanism. The prediction magnitude for on-line error compensation was acquired through the real-time regression calculation and a corresponding system was developed with output control strategy for the compensation process. To demonstrate the procedure of the proposed approach, an experiment was conducted on the self-construction gantry double direct feed axis test rig. the experimental results show that the method for thermal deformation error compensation reduces the linear feed axis thermally induced error by 75%.