Incidental capture of seabirds in longline fishing gear is a central issue in the conservation of many long-lived marine species. Despite growing evidence of climate-induced effects on population trends of long-lived species, climate change remains generally overlooked in most risk assessments of seabirds. Because variation in climate may interact with the detrimental effects of bycatch, considering climate is of great importance, especially in the context of ongoing global warming. This paper examines the combined effects of bycatch and climate change on the persistence of one of the world’s rarest birds, the Amsterdam Albatross Diomedea amsterdamensis, which has a single population in the upland plateau of Amsterdam Island (Southeast Indian Ocean). Using continuous monitoring from 1983 onwards, we first estimated the relationship between climate and the species’ demographic parameters. We then built a stochastic matrix population model to estimate the population growth rate and the probability that the population declines below the level recorded in 1983 of nine breeding pairs under different scenarios involving the joint effects of additional mortality caused by longline fisheries and climate change. The results suggest that the demography of the Amsterdam Albatross is influenced by climate in both breeding and wintering grounds and that these relationships may to some extent compensate for the impact of additive bycatch mortality. However, these compensatory effects would be negligible if the annual additional mortality exceeds around six individuals per year, suggesting that the resumption of longline fishery in the foraging range of the Amsterdam Albatross would rapidly put this species at risk of extinction.