The forest fire occurrence prediction model is a very useful tool for preventing and extinguishing forest fires. The determination of forest fire drivers is important for establishing a high-precision forest fire prediction model. In this paper, we studied the relative influence of different types of factors on forest fire occurrence in forest areas of Jiangxi Province. Several models, i.e., Multilayer perceptron (MLP), Logistic, and Support vector machine (SVM), are used to predict the occurrence of forest fires. Through modeling and analysis of forest fire data from 2010 to 2016 years, we found that climatic and topographic are influential factors in the model of forest fire occurrence in Jiangxi Province. Subsequently, we established the MLP occurrence model based on the significant factors after the variable screening. Using ROC plots to compare the effects of the three models, MLP scored 0.984, which was higher than Logistic of 0.933 and SVM of 0.974. For the independent validation set of 2017-2018, an accuracy of 91.73% was also achieved. Therefore, the multilayer perceptron is well suited for the prediction of forest fires in Jiangxi Province. Based on the prediction results, a fire risk level map of Jiangxi Province was produced. Finally, we analyzed the changes in forest fire quantity under climate change, which can be helpful for fire prevention and suppression of forest fires.