Streamflow depends directly on climate conditions (e.g., precipitation and potential evapotranspiration, or E_p), which affect water balance at the basin scale. The present study was conducted to investigate the impact of climate change on streamflow in the Luan River basin, China. To assess the impact of climatic variation on streamflow, the temporal trends of streamflow were explored using the Mann-Kendall method and the sensitivities of streamflow to precipitation, potential evapotranspiration, and the aridity index were evaluated with the modified method of climate elasticity. The results showed that the average coefficients of sensitivity of streamflow to precipitation and potential evapotranspiration were 3.23 and -2.23, respectively, indicating that a 10% increase in precipitation or potential evapotranspiration would lead to a 32.3% increase or a 22.3% decrease in streamflow, respectively. Additionally, the average coefficient of sensitivity of streamflow to the aridity index was -2.53, which indicated that streamflow would decrease by 25.3% with a 10% increase in the aridity index. The average coefficients of the sensitivity of streamflow to climatic variation appeared to have an inverse relationship with the runoff coefficient, showing that the lower the streamflow of the basin became, the more sensitive the streamflow would be with respect to climatic variation.