Leptocybe invasa is a globally invasive pest of eucalyptus plantations, and is steadily spread throughout China. Predicting the growth area of L. invasa in China is beneficial to the establishment of early monitoring, forecasting, and prevention of this pest. Based on 194 valid data points and 21 environmental factors of L. invasa in China, this study simulated the potential distribution area of L. invasa in China under three current and future climate scenarios (SSPs1–2.5, SSPs2–3.5, and SSPs5–8.5) via the MaxEnt model. The study used the species distribution model (SDM) toolbox in ArcGIS software to analyze the potential distribution range and change of L. invasa. The importance of crucial climate factors was evaluated by total contribution rate, knife-cut method, and environmental variable response curve, and the area under the receiver operating characteristic (ROC) curve was used to test and evaluate the accuracy of the model. The results showed that the simulation effect of the MaxEnt model is excellent (area under the ROC curve (AUC) = 0.982). The prediction showed that L. invasa is mainly distributed in Guangxi, Guangdong, Hainan, and surrounding provinces, which is consistent with the current actual distribution range. The distribution area of the potential high fitness zone of L. invasa in the next three scenarios increases by between 37.37% and 95.20% compared with the current distribution. Climate change affects the distribution of L. invasa, with the annual average temperature, the lowest temperature of the coldest month, the average temperature of the driest season, the average temperature of the coldest month, and the precipitation in the wettest season the most important. In the future, the core areas of the potential distribution of L. invasa in China will be located in Yunnan, Guangxi, Guangdong, and Hainan. They tend to spread to high latitudes (Hubei, Anhui, Zhejiang, Jiangsu, and other regions).