To improve the precision of robot machining, a deformation error prediction method for industrial robots based on error superposition, Deformation Error Prediction Fusion Model (DEPFM), is proposed in this paper. Based on the approximate linear relationship between the external force and the deformation error of the robot, the superposition principle of the deformation error is derived. Based on the Extreme Learning Machine (ELM), a Deformation Error Prediction sub-Model (DEPsM) is established, which is suitable for special external force. Finally, DEPsM is fused to get DEPFM for any external force according to the superposition principle of deformation errors. After verifying its effectiveness through simulation, the deformation error prediction experiment is carried out on an industrial robot, and the DEPFM is compared with the traditional stiffness model. The experimental results show that DEPFM can accurately predict the deformation error of the robot with the average prediction error of 30 \(\upmu {\rm m}\) and the prediction accuracy of 93.7%. Compared with the traditional stiffness model, the average prediction error is reduced by 63.8%.