Changes in temperature and precipitation significantly affect plant growth and system function in the alpine ecosystem. As an important reflection of grassland system function, grassland productivity is very sensitive to climate change, especially to temperature and precipitation. Therefore, it is significant to explore how grassland productivity responds to climate change for predicting system function in the alpine steppe under the background of future climate change. Previous studies often investigated the effects of climate change on grassland productivity at annual or seasonal scales, but there was a lack of correlation analysis at finer time scales. Based on the long-term productivity records and corresponding climatic data from 1997 to 2020, we used simple linear regression and partial least squares regression to reveal the responses of grassland productivity to temperature and precipitation on a daily scale. The results showed that: (1) the annual mean temperature and precipitation in the study area increased significantly in the past 24 years, with a rate of 0.03 ℃/a and 4.36 mm/a, respectively. (2) Meanwhile, grassland productivity increased significantly, with a rate of 5.24 g m^-2 a^-1, and had significantly positive responses to annual mean temperature and precipitation variation. (3) The results of the daily analysis showed that the effects of temperature and precipitation during different periods on grassland productivity were different. In specific, the temperature from May to August and September to October and precipitation from May to July and September to November were key periods to explain the impacts of climate change on grassland productivity, especially temperature (May to August) and precipitation (May to July) variations during the growing season had the higher impacts on grassland productivity, suggesting climate change in the growing season was the main driving factor for variation in grassland productivity. Overall, the present study indicated that increasing temperature and precipitation during the growing season in the past 24 years significantly promoted grassland productivity of the alpine steppe. The effects of warm-wet climate on alpine grassland ecosystem function (e.g., grassland productivity) were closely dependent on the magnitude, direction, and synchronization of altered temperature and precipitation.