Sinadoxa corydalifolia is a perennial grass with considerable academic value as a rare species owing to habitat destruction and a narrow distribution. However, its distribution remains unclear. In this study, we predicted the distribution of Sinadoxa corydalifolia in the three-river region (the source of the Yangtze River, Yellow River, and Lancang River) under the context of climate change using the maximum entropy (MaxEnt) model. Under the current climate scenario, the suitable distribution mainly occurred in Yushu County and Nangqian County. The suitable distribution area of Sinadoxa corydalifolia covered 3107 km2, accounting for 0.57% of the three-river region. The mean diurnal air temperature range (Bio2), temperature seasonality (Bio4), and mean air temperature of the driest quarter (Bio9) contributed the most to the distribution model for Sinadoxa corydalifolia, with a cumulative contribution of 81.4%. The highest suitability occurred when air temperature seasonality (Bio4) ranged from 6500 to 6900. The highest suitable mean air temperature of the driest quarter ranged from −5 to 0 °C. The highest suitable mean diurnal temperature (Bio2) ranged from 8.9 to 9.7 °C. In future (2041–2060) scenarios, the suitable distribution areas of Sinadoxa corydalifolia from high to low are as follows: representative concentration pathway (RCP)26 (6171 km2) > RCP45 (6017 km2) > RCP80 (4238 km2) > RCP60 (2505 km2). In future (2061–2080) scenarios, the suitable distribution areas of Sinadoxa corydalifolia from high to low are as follows: RCP26 (18,299 km2) > RCP60 (11,977 km2) > RCP45 (10,354 km2) > RCP80 (7539 km2). In general, the suitable distribution will increase in the future. The distribution area of Sinadoxa corydalifolia will generally be larger under low CO2 concentrations than under high CO2 concentrations. This study will facilitate the development of appropriate conservation measures for Sinadoxa corydalifolia in the three-river region.