It remains unclear whether and how the sensitivity of alpine plant growth to climate change may vary with distance away from the altitudinal distribution center of a vegetation type. On the basis of measurements of aboveground net primary productivity (ANPP) in an alpine Kobresia meadow across 7 altitudes along the southern slope of Nyainqentanglha Mountains in Tibet during 2009-2013, we established a linear regression model between ground ANPP and satellite vegetation index (MODIS NDVI). Using the long time-series MODIS NDVI data, we then applied the established model to estimate ANPP in the study area during 2000-2013. In combination with climatic data obtained from altitudinal HOBO weather stations (2006-2013) and Damxung weather station (2000-2013), we aimed to clarify the altitudinal pattern in the sensitivity of ANPP to changes in temperature and precipitation in alpine meadows. A unimodal pattern in multi-year mean ANPP was observed along the altitudes; ANPP increased with increasing altitude up to 4893-4942 m and then decreased, demonstrating the altitudinal distribution center of the alpine meadow at mid-altitude. ANPP was positively correlated with growing season precipitation but negatively correlated with growing season mean air-temperature during 2000-2013. The absolute values of the linear regression slopes (referred to as the sensitivity of ANPP to changes in precipitation and temperature) showed a pattern opposite to the change in ANPP along the altitudes. The precipitation and temperature sensitivities of ANPP were the lowest around the distribution center but higher at lower or higher altitudes with distance away from the distribution center. In conclusion, our data identified the altitudinal pattern in sensitivity of alpine meadow ANPP to climate change with a link to the altitudinal distribution center of the alpine meadow. Such knowledge is important for understanding the response of alpine meadow ecosystems to future climate change in different environments along an altitudinal gradient.