Rumors in social media not only affect the health of online social networks, but also reduce the quality of information accessed by social media users. When emergencies occur, the rapid spread of rumors can even trigger mass anxiety and panic. However, the existing studies did not make a clear distinction between rumor and non-rumor information in public emergencies, so that they cannot effectively predict the rumor retweeting behavior. To this end, a model for predicting rumor retweeting behavior is presented based on the convolutional neural networks (CNN) called R-CNN model in the paper. In this model, the rumor retweeting behavior is considered as an important driving force of increasing the depth and breadth of rumor cascades, and four feature vectors are constructed with the historical textual content published by users, consisting of attention to public emergencies, attention to rumors, reaction time and tweeting frequency. To input the quantitative feature vectors for R-CNN, a K-means based core tweets extraction method is proposed to select the right tweets, and the quantitative feature representations are proposed. The predictive capability of the model has been proved by experiments base on two rumor datasets of emergencies crawled from Sina weibo. Experimental results indicate that the prediction accuracy of the model reaches 88%, and it can be improved by 7% on average compared with other models. INDEX TERMS Behavior prediction, convolutional neural networks, public emergency, rumor.