Understanding the effects of climate change on potato yield is vital for food security in northwest China. Based on the long-term data of yields and meteorology, this study analysed the impacts of recent climate change on potato yields at a provincial scale in northwest China. The first difference method was used to disentangle the contributions of climate change from the changes in potato yield in two consecutive years. The moving average method was used to decouple the climate-induced yield of potato. The results showed that the yield and planting area of potato from the period 1982 to 2015 increased markedly, with inter-annual fluctuations. The temperature increased significantly during the potato growing period in northwest China, while other climatic factors did not change significantly. Specifically, the changing trends in climatic factors varied among different provinces. The key meteorological factors limiting potato yield were temperature, precipitation and diurnal temperature range, varying in the different provinces. Potato yields in Gansu, Shaanxi, Ningxia and Xinjiang decreased by 127, 289, 199 and 339 kg ha−1, respectively, for every 1 °C increase in daily maximum temperature. The potato yield in Xinjiang decreased by 583 kg ha−1 for every 1 °C increase in daily minimum temperature. For every 100 mm increase in precipitation, the potato yields in Gansu, Qinghai and Ningxia increased by 250, 375 and 182 kg ha−1, respectively. Combining the first difference method and the moving average method, precipitation was the dominant climatic factor affecting potato yield in rain-fed areas (Gansu, Qinghai and Ningxia). For areas with irrigation (Xinjiang) or relatively high rainfall (Shaanxi), maximum temperature was the deciding climatic factor affecting potato yield. Appropriate adaptation to climate change in the different regions will help to ensure potato production in northwest China.