Robinia pseudoacacia is a native tree species on the Loess Plateau, which has excellent functions of soil and water conservation, and carbon sequestration. Large scale afforestation was carried out in the practice of ecological restoration in the Loess Plateau, and the area of Robinia pseudoacacia forest accounted for more than 90% of artificial afforestation in the gully and hilly areas. However, Robinia pseudoacacia forest degenerated in some areas because climate suitability of Robinia pseudoacacia was not considered during afforestation. In this study, MaxEnt (maximum entropy model) was used to simulate the climate suitability and sensitivity of Robinia pseudoacacia on the Loess Plateau in 1961-1990, 1966-1995, 1971-2000, 1976-2005, 1981-2010, and 2100 (under the climate scenarios of Representative concentration pathway RCP4.5 and RCP8.5, respectively) at the spatial resolution of 0.5 km × 0.5 km. The simulation results showed that the distribution and dynamic changes of Robinia pseudoacacia on the Loess Plateau were mainly affected by the coldest month temperature, extreme low temperature, annual precipitation, annual radiation and other climate factors. Low temperature (the coldest month temperature, extreme low temperature) was the most important factor affecting Robinia pseudoacacia. The natural environment was not suitable for Robinia pseudoacacia forest in the northwest and the north of the Loess Plateau, but it was suitable in the southeast (the Guanzhong Plain and the south of Shanxi Province) of the Loess Plateau. Compared with the period of 1961-1990, the geographical distribution pattern of Robinia pseudoacacia forest was basically unchanged during 1961-2010, and its geographical distribution pattern was not significantly changed under the climate scenarios of RCP4.5 and RCP8.5. Overlay analysis showed that climate suitability (namely exist probability) of Robinia pseudoacacia changed significantly. The regions in the west and north of the Loess Plateau were not suitable for Robinia pseudoacacia, where belonged to non-sensitive areas. The regions in the east and southeast were suitable for Robinia pseudoacacia, where was very sensitive to climate change, especially in the south central of Shanxi Province and the Guanzhong Plain in Shaanxi Province, showing significant climate vulnerability. This study has important reference value for choosing suitable area for afforestation, optimizing the spatial distribution of plantation, coping with climate change risk, maintaining the sustainable and healthy development of forest ecosystem on the Loess Plateau.