Global climate warming has profoundly affected terrestrial ecosystems. The Tibetan Plateau (TP) is an ecologically vulnerable region that emerged as an ideal place for investigating the mechanisms of vegetation response to climate change. In this study, we constructed an annual synthetic NDVI dataset with 500 m resolution based on MOD13A1 products from 2000 to 2021, which were extracted by the Google Earth Engine (GEE) and processed by the Kalman filter. Furthermore, considering topographic and climatic factors, a thorough analysis was conducted to ascertain the causes and effects of the NDVI’s spatiotemporal variations on the TP. The main findings are: (1) The vegetation coverage on the TP has been growing slowly over the past 22 years at a rate of 0.0134/10a, with a notable heterogeneity due to its topography and climate conditions. (2) During the study period, the TP generally showed a “warming and humidification” trend. The influence of human activities on vegetation growth has exhibited a favorable trajectory, with a notable acceleration observed since 2011. (3) The primary factor influencing NDVI in the southeastern and western regions of the TP was the increasing temperature. Conversely, vegetation in the northeastern and central regions was mostly regulated by precipitation. (4) Combined with the principal component analysis, a PCA-CNN-LSTM (PCL) model demonstrated significant superiority in modeling NDVI sequences on the Tibetan Plateau. Understanding the results of this paper is important for the sustainable development and the formulation of ecological policies on the Tibetan Plateau.