Globally, the grey-headed albatross Thalassarche chrysostoma is listed as Endangered due to decreasing populations at its major breeding colonies. We analysed the population trend at Marion Island using annual counts of incubating pairs and fledglings from 1984 to 2021 and three methods: TRends and Indices for Monitoring data (TRIM), a generalized additive model and a state-space model. In contrast to rapid decreases at most other colonies, all three methods indicated a local population increase at an average annual rate of 1.3%. The latter two models indicated a decreasing trend from 1997 to 2002, presumably related to mortality on longlines set for Patagonian toothfish Dissostichus eleginoides around the island, which peaked from 1996 to 1998. Grey-headed albatrosses exhibit greater variation in annual counts than other seabird species at Marion Island, possibly linked to interannual variation in breeding success because they are biennial breeders. However, breeding success alone was not significant in any of the models, presumably because it cannot capture the complexities of both population processes and environmental variation. Although all three models predicted the overall trends well, integrated population models, which can account for demographic processes, might be more appropriate to model long-term population trends.