The measurement of residual stresses by the hole-drilling method has been commonly used to evaluate residual stresses in structural members. In this method, eccentricity can usually occur between the hole center and rosette gage center. In this study, the error due to the hole eccentricity is predicted using the artificial neural network. The neural network has trained training examples of stress ratio, normalized eccentricity, off-centered direction and stress error using backpropagation learning process. The prediction results of the error using the trained neural network are good agreement with FE analyzed ones.