Demographic change lies at the core of debates on genetic inheritance and resilience to climate change of prehistoric hunter-gatherers. Here we analyze the radiocarbon record of Iberia to reconstruct long-term changes in population levels and test different models of demographic growth during the Last Glacial-Interglacial transition. Our best fitting demographic model is composed of three phases. First, we document a regime of exponential population increase during the Late Glacial warming period (c.16.6-12.9 kya). Second, we identify a phase of sustained population contraction and stagnation, beginning with the cold episode of the Younger Dryas and continuing through the first half of the Early Holocene (12.9-10.2 kya). Finally, we report a third phase of density-dependent logistic growth (10.2-8 kya), with rapid population increase followed by stabilization. Our results support a population bottleneck hypothesis during the Last Glacial-Interglacial transition, providing a demographic context to interpret major shifts of prehistoric genetic groups in south-west Europe.