The occurrence of software security issues can cause serious consequences in most cases. Early detection of security issues is one of the key measures to prevent security incidents. Security bug report prediction (SBR) can help developers identify hidden security issues in the bug tracking system and fix them as early as possible. However, since the number of security bug reports in real software projects is small, and the features are complex (i.e., there are many types of security vulnerabilities with different types of features), this makes the manual extraction of security features relatively difficult and lead to low accuracy of security bug report prediction with traditional machine learning classification algorithms. To solve this problem, a deep-learning-based security bug report prediction method is proposed. The text mining models TextCNN and TextRNN via deep learning are used to construct security bug report prediction models. For extracting textual features of security bug reports, the Skip-Gram method is used to construct a word embedding matrix. The constructed model has been empirically evaluated on five classical security bug report datasets with different scales. The results show that the deep learning model is superior to the traditional machine learning classification algorithm in 80% of the experimental cases, and the performance of the constructed models can improve 0.258 on average and 0.535 at most in terms of F1-score performance measure. Furthermore, different re-sampling strategies are applied to deal with class imbalance problem in gathered SBR prediction datasets, and the experiment results are discussed.