Much attention has focused on the effects of precipitation (P) and temperature (T) changes on runoff (R); however, the impacts of other climatic factors need to be studied further. Moreover, the monthly and seasonal scale also need to be investigated. In this paper, we investigated the characteristics of changes in annual, seasonal, and monthly hydroclimatic variables, including R, P, T, sunshine duration (SD), relative humidity (RH), and wind speed (WS), between 1956 and 2015 in the Hutuo River basin (HTRB) using the nonparametric Mann-Kendall test, the cumulative anomaly test and the Precipitation-Runoff double cumulative curve method. Additionally, we assessed the contributions of climatic factors to changes in R in the HTRB between 1956 and 2015 using the climate elasticity method. The results indicated that significant downward trends were found for both annual and seasonal R, SD, RH, and WS. In contrast, there was a nonsignificant decrease in annual P; specifically, P significantly increased in spring and winter, but P insignificantly decreased in summer and autumn. Annual and seasonal T increased significantly. The annual R showed an abrupt change in 1979; thus, the entire study period from 1956 to 2015 was divided into two periods: the baseline period (i.e., 1956–1978) and the change period (i.e., 1979–2015). The elasticities in the climatic factors were calculated using the climate elasticity method, and the elasticity values of P, T, SD, RH, and WS were 1.84, −1.07, −2.79, 1.73, and −0.45, respectively. Increasing T was the main cause of the decline in R, and decreasing SD had a large negative contribution to the decline in R in the HTRB. This study will help researchers understand the interactions between climate change and hydrological processes at the basin scale and promote water resource management and watershed planning.