The health insurance industry in China is undergoing great shocks and profound impacts induced by the worldwide COVID-19 pandemic. Taking for instance the three dominant listed companies, namely, China Life Insurance, Ping An Insurance, and Pacific Insurance, this paper investigates the equity performances of China's health insurance companies during the pandemic. We firstly construct a stock price forecasting methodology using the autoregressive integrated moving average, back propagation neural network, and long short-term memory (LSTM) neural network models. We then empirically study the stock price performances of the three listed companies and find out that the LSTM model does better than the other two based on the criteria of mean absolute error and mean square error. Finally, the above-mentioned models are used to predict the stock price performances of the three companies.