Studies on artificial neural networks rarely address both vanishing gradients and overfitting issues. In this study, we follow the pupil learning procedure, which has the features of interpreting, picking, understanding, cramming, and organizing, to derive the pupil learning mechanism (PLM) by which to modify the network structure and weights of 2-layer neural networks (2LNNs). The PLM consists of modules for sequential learning, adaptive learning, perfect learning, and less-overfitted learning. Based upon a copper price forecasting dataset, we conduct an experiment to validate the PLM module design modules, and an experiment to evaluate the performance of PLM. The empirical results indeed approve the PLM module design and show the superiority of the proposed PLM model over the linear regression model and the conventional backpropagation-based 2LNN model.