Three-River-Source (TRS) National Park stands as one of China’s earliest established national parks, dedicated to significant ecological responsibilities that include conserving soil and water resources in the Tibetan Plateau region. Research on climate change’s influence on the TRS region’s grasslands is of great significance in our efforts to comprehend and conserve the grassland ecosystem. The most effective random forest (RF) model was chosen to invert the aboveground biomass (AGB) of grassland in the previous 6 years (2015−2020) and predict the grassland AGB in the following 20 years (2021−2040) by comparing linear regression and multivariate nonlinear regression models such as RF, support vector machine, decision tree, and artificial neural network. A Theil–Sen median trend analysis and a Mann–Kendal test were then used to examine the trends of grassland AGB. The results showed that (1) RF outperformed other models in estimating grassland AGB, with a test set decision coefficient of multiple determination (R2) of 0.722, a root mean square error of 42.596 g/m2, and a mean absolute error of 35.619 g/m2; (2) over 6 years, the grassland AGB in TRS National Park had a spatial trend of a steady rise from the northwest to the southeast. The average annual grassland AGB was 247.333 g/m2, with averages of 44.836 g/m2, 92.601 g/m2, and 120.217 g/m2 in the Yangtze River, Yellow River, and Lancang River source parks respectively. The trend of the grassland AGB was primarily stabilized and slightly recovered, with a small portion of the slightly deteriorated areas; (3) climate change significantly affected grassland AGB, and when temperature and precipitation conditions were adequate, grassland AGB values increased with temperature and precipitation. In the scenarios of ssp119, ssp245, and ssp585, grassland AGB is projected to exhibit a dynamic upward trend over the next 20 years. Global warming is expected to boost grassland AGB. Comprehensive measures are essential to maintain grassland health and ensure a positive impact on global carbon and ecological balance. The study’s findings hold great importance for the ecological security of the TRS region and contribute to our global understanding of sustainable grassland development.