Climate change involves modifications in both the mean and the variability of temperature and precipitation. According to global warming projections, both the magnitude and the frequency of extreme weather events are increasing, thereby increasing climate variability. The previous studies have reported that climate warming tends to decrease biodiversity and the temporal stability of community primary productivity (i.e., community stability), but the effects of the variability of temperature and precipitation on biodiversity, community stability, and their relationship have not been clearly explored. We used a long-term (from 1982 to 2014) field data set from a temperate grassland in northern China to explore the effects of the variability of mean temperature and total precipitation on species richness, community stability, and their relationship. Results showed that species richness promoted community stability through increases in asynchronous dynamics across species (i.e., species asynchrony). Both species richness and species asynchrony were positively associated with the residuals of community stability after controlling for its dependence on the variability of mean temperature and total precipitation. Furthermore, the variability of mean temperature reduced species richness, while the variability of total precipitation decreased species asynchrony and community stability. Overall, the present study revealed that species richness and species asynchrony promoted community stability, but increased climate variability may erode these positive effects and thereby threaten community stability.