It is of great significance to carry out the research on the changes of National Park ecosystem services and the trade-off and synergy to realize the strictest ecological protection, promote the construction of ecological civilization and realize the sustainable development of the region. In this paper, the Three-River-Source National Park was taken as an example. Firstly, the terrestrial ecosystem service accounting method was used to measure the ecosystem services (including 4 kinds and 11 types) from 1990 to 2015, and we revised the accounting results by using the contribution rate of ecosystem services value. Then the characteristics of its temporal and spatial changes during the study period were analyzed. Finally, the trade-off/synergy relationships among multiple ecosystem services were quantitatively analyzed based on bivariate local spatial autocorrelation and correlation coefficient in different periods. The results showed that: (1) The value of the ecosystem services of the Three-River-Source National Park increased from 54.237 billion in 1990 to 83.47 billion in 2015, an increase of 29.233 billion, or up by 53.90%, and the average growth rate at each stage was 9.01%. The value ratio of ecosystem services of the Changjiang and Huanghe river source national parks is consistent with the overall situation of the park, and the water areas provided the highest value of ecosystem services, followed by grassland and wetland. Grassland and water supply more than 90% of the ecological services of the park. But the grasslands provided the highest (70.58%) value of ecosystem services in the Lancang River Source National Park, and followed by wetlands (23.58%) and water areas (3.38%). (2) The ecosystem services value increased from northwest to southeast in Changjiang and Lancang river source national parks, but the ecosystem services value presented the characteristics of "higher in the east but low in the west" in Huanghe River Source National Park. Correlation analysis showed that synergy was the dominate relationship among ecosystem services in the Three-River-Source National Park, but the correlation degree among ecosystem services varied. (3) In quantity, the global Moran′s I index and the correlation coefficient of the trade-off and synergy among the four typical ecological services were consistent. And there was significant heterogeneity of trade-off/synergy relationships among multiple ecosystem services in terms of spatial pattern.