Vegetation is the main body of the terrestrial ecosystem and is a significant indicator of environmental changes in the regional ecosystem. As an essential link connecting South Asia and Southeast Asia, the Lancang-Mekong River Basin(LMRB) can provide essential data support and a decision-making basis for the assessment of terrestrial ecosystem environmental changes and the research and management of hydrology and water resources in the basin by monitoring changes in its vegetation cover. This study takes the Lancang-Mekong River Basin as the study area, and employs the Sen slope estimation, Mann–Kendall test, and Hurst exponent based on the MODIS NDVI data from 2000 to 2021 to study the spatial and temporal evolution trend and future sustainability of its NDVI. Besides, the nonlinear characteristics such as mutation type and mutation year are detected and analyzed using the BFAST01 method. Results demonstrated that: (1) In the past 22 years, the NDVI of the Lancang-Mekong River Basin generally exhibited a fluctuating upward trend, and the NDVI value in 2021 was the largest, which was 0.825, showing an increase of 4.29% compared with 2000. However, the increase rate was different: China has the most considerable NDVI growth rate of 7.25%, followed by Thailand with an increase of 7.21%, Myanmar and Laos as the third, while Cambodia and Vietnam have relatively stable vegetation changes. The overall performance of NDVI is high in the south and low in the north, and is dominated by high and relatively high vegetation coverage, of which the area with vegetation coverage exceeding 0.8 accounts for 62%. (2) The Sen-MK trend showed that from 2000 to 2021, the area where the vegetation coverage in the basin showed a trend of increase and decrease accounted for 66.59% and 18.88%, respectively. The Hurst exponent indicated that the areas where NDVI will continue to increase, decrease, and remain unchanged in the future account for 60.14%, 25.29%, and 14.53%, respectively, and the future development trend of NDVI is uncertain, accounting for 0.04%. Thus, more attention should be paid to areas with a descending future development trend. (3) BFAST01 detected eight NDVI mutation types in the Lancang-Mekong River Basin over the past 22 years. The mutations mainly occurred in 2002–2018, while 2002–2004 and 2014–2018 were the most frequent periods of breakpoints. The mutation type of “interruption: increase with negative break” was changed the most during this period, which accounts for 36.54%, and the smallest was “monotonic decrease (with negative break)”, which only accounts for 0.65%. This research demonstrates that combining the conventional trend analysis method with the BFAST mutation test can more accurately analyze the spatiotemporal variation and nonlinear mutation of NDVI, thus providing a scientific reference to develop ecological environment-related work.