The outbreak of Mpox in China has rendered the promotion of effective preventive measures among susceptible populations particularly crucial. The study team investigated 2,403 men who have sex with men (MSM) for whether they would get a Mpox vaccine. The participants were randomly split into a training set and a testing set in a ratio of 3:1 with R software. The variables were screened by the Least Absolute Shrinkage and Selection Operator (LASSO) regression analysis. Then, the prediction model, including important variables, used a multivariate logistic regression analysis and presented as a nomogram. The Receiver Operating Characteristic (ROC) curve, Calibration curve, Kolmogorov-Smirnov (K-S) test, Lift test and Population Stability Index (PSI) were performed to test the validity and stability of the model. 87.1% of the participants had vaccination intentions. Five of the thirty-one screened variables, i.e., Mpox knowledge, social support, vaccination internal rewards, vaccination external rewards and vaccination response efficacy, were included in the prediction model. The results indicated that the model has a high predictive power and is highly stable. The government should design targeted public health strategies, integrating social engagement and leveraging peer and community education for Mpox vaccine promotion.