In the past few years, with the development of information technology and the focus on information security, many studies have gradually been aimed at data hiding technology. The embedding and extraction algorithms are mainly used by the technology to hide the data that requires secret transmission into a multimedia carrier so that the data transmission cannot be realized to achieve secure communication. Among them, reversible data hiding (RDH) is a technology for the applications that demand the secret data extraction as well as the original carrier recovery without distortion, such as remote medical diagnosis or military secret transmission. In this work, we hypothesize that the RDH performance can be enhanced by a more accurate pixel value predictor. We propose a new RDH scheme of prediction-error expansion (PEE) based on a multilayer perceptron, which is an extensively used artificial neural network in plenty of applications. The scheme utilizes the correlation between image pixel values and their adjacent pixels to obtain a well-trained multilayer perceptron so that we are capable of achieving more accurate pixel prediction results. Our data mapping method based on the three-dimensional prediction-error histogram modification uses all eight octants in the three-dimensional space for secret data embedding. The experimental results of our RDH scheme show that the embedding capacity greatly increases and the image quality is still well maintained.