Meteorological disasters will not only bring huge economic losses, but also cause the outbreak of public opinion and even social panic.The Internet era brings opportunities as well as challenges to the governance of public opinion.In recent years, Long Short-Term Memory network (LSTM) has shown advantages in text sentiment analysis, yet it has problems such as incomplete semantics and low accuracy in feature extracting.Convolutional Neural Network (CNN) has been introduced to make up for this shortcoming, but it still cannot considere the syntactic dependence between words.Here, we combine LSTM and Broad Learning System (BLS) with incremental learning algorithm as its core, and thus propose an LSTM-BLS text sentiment analysis model.Then the 2020 cold wave event with gale process and great temperature drop in central and eastern China is taken as an example to analyze the public sentiment tendency when sudden meteorological disasters occur.The results show that the proposed LSTM-BLS reaches a high accuracy of 97.42%, which is 17.23 and 13.46 percentage points higher than the baseline models of K-means and Support Vector Machine (SVM), respectively, and 7.13 and 4.17 percentage points higher than the existing deep learning models of LSTM and CNN-LSTM, respectively.