Glaciers have been recognized as the most sensitive indicators of climate change. Mountainous areas, with their characteristic snow and glacier cover, have long been recognized as special hydrological environments, receiving above-average amounts of precipitation. The streams originating in the mountains, nourished with distinct seasonal variations, provide water for the populations of the adjacent lowland. Little is known about the effect of climate change on snow and glacier hydrology and glacier mass balance in the Laohugou Glacier Basin (LHGB) over the past 50 years. A study of the glacier basin was performed to quantify the expected impact of climate change on the hydrology in the north-eastern Qinghai-Tibet Plateau. The DEM (Digital Elevation Model) data, daily temperature, daily precipitation, and evaporation data were applied to force the HBV (Hydrologiska Byrans Vattenbalansavdelning)-light conceptual model to simulate runoff depth and glacier mass balance in the historical period (1959–2015). A genetic calibration algorithm approach (GAP method) was used to obtain parameter sets that reproduced observed runoff depth well. The results suggested a drastic increase of the runoff depth from 1995 to 2015 in the Laohugou glacier basin driven by increased temperature. Temperature and precipitation increased by 0.40 °C (10a)−1 and 1.6 mm·a−1 (p < 0.01), respectively, at AWS1 (the automatic weather station at 4192 m a.s.l. near the hydrological station) in the LHGB from 1959 to 2015. The simulated runoff depth increased at 5.7 mm·a−1 (p < 0.01), the glacier mass balance (GMB) of the LHGB was −280.5 mm·a−1, and the overall glacier mass balance was −17.55 m w.e. from 1959 to 2015. The runoff is found to be more sensitive to the variation of temperature than the variation of precipitation. When the glacier area is decreased by 10%, 53%, and 100%, the peak runoff (July) decreased by 20.4%, 54.2%, and 72.3% relative to the baseline, respectively. In the future climate, the function of glaciers in compensating a potential low flow and regulating peak flow will be weakened in the critical months.