In the context of global warming, there may be different responses of radial growth of tree species to climate change. In this paper, tree-ring cores were collected from two dominant trees, Pinus tabulaeformis and Picea crassifolia, on Changling Mountain located in the eastern region of the Qilian Mountains. In total, 147 cores were extracted from 70 Pinus tabulaeformis trees, and 111 cores were extracted from 54 Picea crassifolia trees. All cores were collected from healthy, living trees. Two tree-ring width chronologies were developed, and we analyzed the correlation relationship between the two tree-ring width chronologies and climate variables (temperature and precipitation) to determine the different responses of radial growth of two tree species to climate warming. Additionally, the Mann-Kendall method was used to analyze the abrupt change point of the mean temperature and the abrupt change of radial growth of Pinus tabulaeformis and Picea crassifolia to climate and this was discussed. Our results indicated that:(1) The chronology of Pinus tabulaeformis contained more climate information than the chronology of Picea crassifolia, and its mean sensitivity, standard deviation, signal to noise ratio, and expressed population signal were higher than those of the Picea crassifolia chronology; (2) The climatic factors had different degrees of limitation to the radial growth of the two tree species. The radial growth of Pinus tabulaeformis was primarily related to precipitation (September of the previous year and March to August of the current year) and temperature (September of the previous year), but it was more sensitive in its response to precipitation. However, the radial growth of Picea crassifolia was accompanied by the combined effect of temperature (September of the current year) and precipitation (September of the previous year, March and July of the current year); (3) After the abrupt temperature, the correlation between the chronologies of Pinus tabulaeformis and Picea crassifolia and the temperature elements significantly increased, but the correlation between the chronology of Picea crassifolia and temperature was more obvious, which indicated that the radial growth of Picea crassifolia had greater instability in its response to temperature; (4) The drought stress induced by rising the mean minimum temperature in the growing season was the main reason for the change in the radial growth-temperature response of Pinus tabulaeformis and Picea crassifolia.