The spread of rumours on social media in the context of public health emergencies often distorts perceptions of public events and obstructs crisis management. Microblog entries about 28 rumour cases are collected on Sina Weibo during the COVID-19 outbreak. The Modality–Agency–Interactivity–Navigability model is used to identify the key factors of rumour prediction. To investigate the relationship among information modality, information content, information source and rumour identification, the binary logistic regression model is established based on the features of users and microblog entries. In addition, we propose a multi-feature rumour prediction model based on the Bidirectional Encoder Representations from Transformers (BERT) and Extreme Gradient Boosting (XGBoost) models. The proposed rumour prediction model has the best performance compared with other models. The feature importance is then calculated by the SHapley Additive exPlanations (SHAP), which can also explain the XGBoost results. It is shown that the likelihood that microblog entries are rumours decreases as the values of variables such as user influence and the positive sentiment of comments rise. Microblog entries posted on Thursdays or at noon are more probably to be rumours than those posted at other time. The proposed model can assist emergency management departments in establishing a feasible rumour prediction mechanism to guide public opinion against rumours.