Pixel prediction is an important issue in the field of reversible data hiding. Neural networks are gradually used to improve the accuracy of pixel prediction owing to their excellent performance. However, current neural network-based pixel predictors are designed for natural images and do not consider the characteristics of medical images. Therefore, in this paper, we propose a dual-branch neural network-based reversible data hiding scheme for medical images. Detailedly, considering the characteristics of medical images, in which complex and smooth regions are more clearly distinguished, we present a clustering method to classify pixels into three classes according to their complexities, and generate masks to assist pixel prediction. Then, in the prediction stage, a dual-branch neural network-based pixel predictor is designed to extract unique and shared features, and a convolutional block attention module is used to optimize the extracted features. Finally, in the embedding stage, considering the characteristics of region of interest (ROI) and region of non-interest (NROI) in medical images, we design a class-based embedding algorithm, which can prioritize embedding data into NROI with low complexity and then sequentially into low texture complexity region and high texture complexity region of ROI. Experimental results show that our scheme can achieve better performance of pixel prediction and data embedding than existing state-of-the-art works.