To quantitatively assess the impact of climate variability on streamflow in an ungauged mountainous basin is a difficult and challenging work. In this study, a hybrid model combing downscaling method based on earth data products, back propagation artificial neural networks (BPANN) and weights connection method was developed to explore an approach for solving this problem. To validate the applicability of the hybrid model, the Kumarik River and Toshkan River, two headwaters of the Aksu River, were employed to assess the impact of climate variability on streamflow by using this hybrid model. The conclusion is that the hybrid model presented a good performance, and the quantitative assessment results for the two headwaters are: (1) the precipitation respectively increased by 48.5 and 41.0 mm in the Kumarik catchment and Toshkan catchment, and the average annual temperature both increased by 0.1 °C in the two catchments during each decade from 1980 to 2012; (2) with the warming and wetting climate, the streamflow respectively increased 1.5 × 108 and 3.3 × 108 m3 per decade in the Kumarik River and the Toshkan River; and (3) the contribution of the temperature and precipitation to the streamflow, which were 64.01 ± 7.34, 35.99 ± 7.34 and 47.72 ± 8.10, 52.26 ± 8.10%, respectively in the Kumarik catchment and Toshkan catchment. Our study introduced a feasible hybrid model for the assessment of the impact of climate variability on streamflow, which can be used in the ungauged mountainous basin of Northwest China.