Frequent droughts may have negative influences on the ecosystem (i.e., terrestrial vegetation) under a warming climate condition. In this study, the linear regression method was first used to analyze trends in vegetation change (normalized difference vegetation index (NDVI)) and drought indices (Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI)). The Pearson Correlation analysis was then used to quantify drought impacts on terrestrial vegetation in the Weihe River Basin (WRB); in particular, the response time of vegetation to multiple time scales of drought (RTVD) in the WRB was also investigated. The trend analysis results indicated that 89.77% of the area of the basin showed a significant increasing trend in NDVI from 2000 to 2019. There were also significant variations in NDVI during the year, with the highest rate in June (0.01) and the lowest rate in January (0.002). From 2000 to 2019, SPI and SPEI at different time scales in the WRB showed an overall increasing trend, which indicated that the drought was alleviated. The results of correlation analysis showed that the response time of vegetation to drought in the WRB from 2000 to 2019 was significantly spatially heterogeneous. For NDVI to SPEI, the response time of 12 months was widely distributed in the north; however, the response time of 24 months was mainly distributed in the middle basin. The response time of NDVI to SPI was short and was mainly concentrated at 3 and 6 months; in detail, the response time of 3 months was mainly distributed in the east, while a response time of 6 months was widely distributed in the west. In autumn and winter, the response time of NDVI to SPEI was longer (12 and 24 months), while the response time of NDVI to SPI was shorter (3 months). From the maximum correlation coefficient, the response of grassland to drought (SPEI and SPI) at different time scales (i.e., 6, 12, and 24 months) was higher than that of cultivated land, forestland, and artificial surface. The results may help improve our understanding of the impacts of climatic changes on vegetation cover.