Forest fires can cause serious harm. Scientifically predicting forest fires is an important basis for preventing them. Currently, there is little research on the prediction of long time-series forest fires in China. Choosing a suitable forest fire prediction model and predicting the probability of Chinese forest fire occurrence are of great importance to China’s forest fire prevention and control work. Based on fire hotspot, meteorological, terrain, vegetation, infrastructure, and socioeconomic data collected from 2003 to 2016, we used a random forest model as a feature-selection method to identify 13 major drivers of forest fires in China. The forest fire prediction models developed in this study are based on four machine-learning algorithms: an artificial neural network, a radial basis function network, a support-vector machine, and a random forest. The models were evaluated using the five performance indicators of accuracy, precision, recall, f1 value, and area under the curve. We used the optimal model to obtain the probability of forest fire occurrence in various provinces in China and created a spatial distribution map of the areas with high incidences of forest fires. The results showed that the prediction accuracy of the four forest fire prediction models was between 75.8% and 89.2%, and the area under the curve value was between 0.840 and 0.960. The random forest model had the highest accuracy (89.2%) and area under the curve value (0.96); thus, it was used as the optimal model to predict the probability of forest fire occurrence in China. The prediction results indicate that the areas with high incidences of forest fires are mainly concentrated in north-eastern China (Heilongjiang Province and northern Inner Mongolia Autonomous Region) and south-eastern China (including Fujian Province and Jiangxi Province). In areas at high risk of forest fire, management departments can improve forest fire prevention and control by establishing watch towers and using other monitoring equipment. This study helps in understanding the main drivers of forest fires in China, provides a reference for the selection of high-precision forest fire prediction models, and provides a scientific basis for China’s forest fire prevention and control work.