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Elevation dependency and teleconnections are very important for global climate change studies. In this study, the GEV model and Pearson correlation coefficient was used to investigate the relationships between climate extremes and elevations. The results showed no significant relationships in trend magnitudes and elevations for climate extremes. This suggests that elevation dependency is deficient in the arid region of northwestern China. Additionally, teleconnection indices were taken as covariates in the location, scale and shape parameters of the nonstationary generalized extreme value (GEV) model, which was used to test whether climate extremes are influenced by those indices. The covariate of the Northern Hemisphere polar vortex area (VPA), the Tibetan Plateau High (XZH) and the Westerly circulation index (WI) is significantly improved over the GEV model without a covariate. In addition, the Arctic Oscillation (AO), the Siberian High intensity index (SHI) and the North Atlantic Oscillation (NAO) seemed to affect the winter climate. Teleconnections related to climate extremes can be utilized to predict the probability of extreme weather in the arid region of northwestern China.