1. Fisheries can affect non-target species through bycatch, and climate change may act simultaneously on their population dynamics. Estimating the relative impact of fisheries and climate on non-target species remains a challenge for many populations because the spatio-temporal distribution of individuals remains poorly known and available demographic information is incomplete. 2. We used population survey data, capture–mark–recapture methods, population modelling and the demographic invariant method to investigate the effects of climate and fisheries on the demography of a predator species affected by bycatch. These complementary approaches were used to help account for different sources of uncertainty. 3. The white-chinned petrel Procellaria aequinoctialis is the commonest seabird species killed by longline fisheries in the Southern Ocean. Petrel breeding success was positively related to the fishing effort for Patagonian toothfish Dissosticus eleginoides . El Niño events negatively affected adult survival with a time lag of 3 years. Fishing efforts for toothfish and hake ( Merluccius spp.) were negatively related to petrel recruitment, suggesting that fisheries-induced mortality strongly impacted younger age classes. Lambda estimated from matrix population models was below replacement (0·964 ± 0·026), and the number of breeding pairs declined by ≈ 37% in 21 years. This decline was probably caused by low survival of both young age classes and adults. 4. The Crozet archipelago, Southern Indian Ocean, population size was estimated at ≈ 170 000 individuals in the early 1980s, and would be severely affected by any additional source of mortality that approached 8000 individuals per year. The number of petrels killed by the toothfish fishery alone exceeded this threshold during the late 1990s and early 2000s, but has declined well below this since 2003. 5. Synthesis and applications . Complementary approaches suggest that both longline fishery bycatch and climate have a significant impact on the size of the Southern Ocean white-chinned petrel population. Stopping or reversing climate change will be a very slow process, and may be impossible. Therefore, we recommend a reduction in bycatch to help the populations recover. Further information on the status of individuals caught in longlines is required to understand the demographic processes involved.