It is of great importance to investigate links between hydrological drought and climate indices, which helps to further reveal the cause of hydrological drought from a perspective of climate change, thus helping guiding future drought prediction and control. For a case study in the Columbia River basin, the Standardized Streamflow Index (SSI) was employed to characterize hydrological drought. The heuristic segmentation method was applied to identify change points of annual streamflow series spanning 1960–2012 in the Columbia River basin, and the cross‐wavelet analysis was utilized to reveal the correlations between monthly climate indices and SSI. The primary results are as following: (1) monthly SSI has a statistically significantly increasing trend in November and December and a noticeably decreasing trend in June and July in the main stream of the basin; (2) generally, hydrological drought risk in this basin is high, and that in the Snake River is higher than the main stream of the Columbia River; (3) El Niño Southern Oscillation (ENSO) and Arctic Oscillation (AO) play a major role in affecting hydrological drought in the Columbia River basin, and ENSO index mainly affects SSI at a relatively short time scale (2–7 years), while AO primarily impacts SSI at a relatively long time scale (more than 10 years); (4) anthropogenic activities intensify hydrological drought in the Columbia River basin, and they primarily influence the linkages between climate indices and hydrological drought at intra‐annual scale (less than 12 months), however, which do not change the basic pattern of their correlations.