Negative emotion classification refers to the automatic classification of negative emotion of texts in social networks. Most existing methods are based on deep learning models, facing challenges such as complex structures and too many hyperparameters. To meet these challenges, in this paper, we propose a method for negative emotion classification utilizing a Robustly Optimized BERT Pretraining Approach (RoBERTa) and $p$-norm Broad Learning ( $p$-BL). Specifically, there are mainly three contributions in this paper. Firstly, we fine-tune the RoBERTa to adapt it to the task of negative emotion classification. Then, we employ the fine-tuned RoBERTa to extract features of original texts and generate sentence vectors. Secondly, we adopt $p$-BL to construct a classifier and then predict negative emotions of texts using the classifier. Compared with deep learning models, $p$-BL has advantages such as a simple structure that is only 3-layer and fewer parameters to be trained. Moreover, it can suppress the adverse effects of more outliers and noise in data by flexibly changing the value of $p$. Thirdly, we conduct extensive experiments on the public datasets, and the experimental results show that our proposed method outperforms the baseline methods on the tested datasets.