As an essential part of terrestrial ecosystems, convenient and accurate reconstruction of the past carbon sequestration capacity of forests is critical to assess future trends of aboveground carbon storage and ecosystem carbon cycles. In addition, the relationship between climate change and carbon sequestration of forests has been vigorously debated. In this study, dynamic change of carbon sequestration capacity in aboveground biomass of Picea schrenkiana (hereinafter abbreviated as P. schrenkiana) in the Tianshan Mountains, northwestern China, from 1850–2017, were reconstructed using dendrochronology. The main climate drivers that affected carbon sequestration capacity in aboveground biomass of P. schrenkiana were then investigated. The results showed that: (1) tree-ring width and diameter at breast height (DBH) of P. schrenkiana obtained from different altitudes and ages were an effective and convenient estimation index for reconstructing the carbon sequestration capacity of P. schrenkiana. The carbon storage of P. schrenkiana forest in 2016 in the Tianshan Mountains was 50.08 Tg C calculated using tree-ring width and DBH, which was very close to the value determined by direct field investigation data. (2) The annual carbon sequestration potential capacity of P. schrenkiana exhibited an increasing trend from 1850–2017. Temperature, especially minimum temperature, constituted the key climatic driver resulting in increased carbon sequestration capacity. The contribution rates of temperature and minimum temperature to the change of P. schrenkiana carbon sequestration capacity was 75% and 44%, respectively. (3) The significant increase of winter temperature and minimum temperature led to warming in the Tianshan Mountains, resulting in a significant increase in carbon sequestration capacity of P. schrenkiana. The results indicate that, with the continuous increase of winter temperature and minimum temperature, carbon sequestration of P. schrenkiana in the Tianshan Mountains is predicted to increase markedly in the future. The findings of this study provide a useful basis to evaluate future aboveground carbon storage and carbon cycles in mountain systems possessed similar characteristics of the Tianshan Mountains.