Southern bluefin tuna is a highly valuable, severely depleted species, whose abundance and productivity have been difficult to assess with conventional fishery data. Here we use large-scale genotyping to look for parent-offspring pairs among 14,000 tissue samples of juvenile and adult tuna collected from the fisheries, finding 45 pairs in total. Using a modified mark-recapture framework where 'recaptures' are kin rather than individuals, we can estimate adult abundance and other demographic parameters such as survival, without needing to use contentious fishery catch or effort data. Our abundance estimates are substantially higher and more precise than previously thought, indicating a somewhat less-depleted and more productive stock. More broadly, this technique of 'close-kin mark-recapture' has widespread utility in fisheries and wildlife conservation. It estimates a key parameter for management-the absolute abundance of adults-while avoiding the expense of independent surveys or tag-release programmes, and the interpretational problems of fishery catch rates.