The Central Asia is located in the hinterland of Eurasia, with scarce rainfall and uneven distribution of water resources. It is the largest arid zone in the temperate and warm temperate zones of the Northern Hemisphere. The vegetation types in the Central Asia are mainly woodland, grassland and cultivated land, among which grassland occupies absolute superiority in land use types. As one of the most important components of the terrestrial ecosystem, grassland is the means of production and management object of animal husbandry, which plays a key role in maintaining the global carbon cycle, regional ecological security and social stability. With the intensification of global climate change, the effects of drought on the carbon cycle of grassland ecosystems become more complex. As the largest component of global terrestrial ecosystem carbon flux, gross primary productivity (GPP) has profound impact on the overall terrestrial carbon cycle. Therefore, it is of great significance to explore the effects of drought on grassland GPP for understanding the mechanism of regional carbon cycling and maintaining the stable development of grassland ecosystem. This paper takes Central Asia as the research area, and based on NIRv-GPP and SPEI base v.2.7 dataset, uses Theil-Sen Median slope estimation combined with Mann-Kendall significance test, M-K mutation test, and correlation analysis methods to explore the time-lag and cumulative effects of drought on grassland GPP from 1982 to 2018. The results showed that: (1) the annual average GPP and the annual average standardized precipitation evapotranspiration index (SPEI) of grassland in the Central Asia showed a downward trend over time. (2) Drought had a time-lag effect on most grassland (95.6%) in the Central Asia, and the lag time scale was concentrated in 2-3 months. With the aggravation of drought conditions, the lag time became longer, and the effect of lag effect on grassland GPP was weakened. (3) Most grassland (95.8%) in the Central Asia showed cumulative response to drought, and the cumulative time scale was mainly in April, May and October. With the aggravation of drought, the cumulative time became shorter, and the cumulative effect on grassland GPP became stronger. (4) Through comparative study of time-lag effect and cumulative effect, it was found that the time-lag effect of drought on grassland GPP was greater than the cumulative effect in more than three quarters (76.84%) of grassland areas in the Central Asia. The results can provide reference for understanding the dynamic change characteristics of ecological environment and the mechanism of regional carbon cycle in the Central Asia under the background of climate change.