The Kow Swamp people are a fossil population of robust modern humans. We report optically stimulated luminescence (OSL) ages on sediments from Kow Swamp that are at odds with radiocarbon ages obtained previously for the site. The calibrated 14C ages place the Kow Swamp people in the period 15-9 ka. Our single aliquot OSL ages suggest that they lived around the time of the Last Glacial Maximum (LGM) between 22 and 19 ka. An LGM age for the Kow Swamp people is supported by palaeoenvironmental reconstruction. The shoreline silt, in which most of them were interred, was deposited by high lake levels between 26 and 19 ka. Few robust people were left after 19 ka when a sand lunette formed. Climate change may explain the demise of this unusual genetic population.