In this study, we propose a method for constructing an estimation model at the early stage of the building project which attains high accuracy and is robust. In the proposed method, the prediction accuracy is improved over the conventional method by focusing on the outliers and modifying the outliers's data when building the prediction model. More concretely, applying the so-called Winsorization mean and the trimmed mean which are known as statistical methods, the proposed methods appropriately modify the amount which is regarded as an outlier in constructing our prediction model. The method is then applied to two types of mutiple regression (L_2 regression and L_1 regression) and two types of neural network (multiple layer network and radial basis function network). In order to quantitatively evaluate the methods, they are applied to real building construction data. It is observed through the experiments that (i) the data modification is in general effective for improving the overall prediction accuracy, (ii) the Winsorization method is superior to the other data modification methods for any of four prediction models, and (iii) both of L_1 regression and the radial basis function network are superior to the other two.