The Tibetan Plateau is a sensitive area to global climate change, and the special natural environmental conditions have nurtured extremely fragile vegetation and its ecosystems, making it one of the ideal regions to study the response of vegetation to climate change. In this study, we used the drought index (SPEI) and the vegetation index (NDVI) as drought and green indicators, respectively. The spatial and temporal variation patterns of vegetation greenness on the Tibetan Plateau from 1982 to 2015 were analysed, and the response of vegetation greenness to dry and wet changes was investigated. The results showed that the grassland vegetation improved overall (slope = 0.00015, P < 0.05) and degraded locally during 34 years. The NDVI of grassland vegetation showed an increasing trend from 1982 to 2008 (slope = 0.00005, P = 0.86), and a significant decreasing trend from 2009 to 2015 (slope = −0.002, P < 0.05). The degraded areas of grassland NDVI were mainly distributed in wet areas. Meanwhile, the Tibetan Plateau as a whole showed a non-significant trend of increasing drought, with a mitigating trend of drought in dry areas and an increasing trend of drought in wet areas. The probability of vegetation growth loss was higher with increasing drought. The vulnerability of grassland vegetation to drought events was significantly higher in the humid region than in the arid region. Under the current drought intensification, the risk of loss of grassland vegetation to drought in the humid zone will increase. This suggests that we need to pay more attention to the stability of vegetation in the humid region and drought trends.