According to the daily meteorological data of 21 stations from 1960 to 2015 in Weihe River Basin, northwest China,We used Penman-Monteith model,climate inclination rate and Morlet wavelet to study the characteristics of climate change in Weihe River basin. The results showed as follows: (1) Annual temperature was in a slowly rising trend in recent 55 years,in particular,the rate of temperature rising from the middle of the 1980s to the early 1990s was faster than the rate at any other times. The annual precipitation has been slowly declined in recent 55 years. The periods from the middle of the 1980s to the early 1990s and the early 21st century were the major precipitation decreased periods. (2) The results from Morlet wavelet analysis indicated a vibration period scale as 13 years to 15 years for a sub fluctuation and 25 years to 30 years for a main fluctuation about both the extreme drought events and the air temperature,a sub fluctuation of 15 years to 17 years and main fluctuation of 25 years to 30 years about the annual precipitation. It is shown that the changing rules of the three are similar. (3) There are some differences in the climate change characteristics of the research area. The minimal trend of the annual temperature and precipitation is Wuqi-Zhuangtou Basin,and the greatest change trend of annual precipitation and extreme drought events is Tianshui-Xiji Basin. In general,the change of climate elements in the research area are basically consistent.