Historic demography changes of plant species adapted to New World arid environments could be consistent with either the Glacial Refugium Hypothesis (GRH), which posits that populations contracted to refuges during the cold-dry glacial and expanded in warm-humid interglacial periods, or with the Interglacial Refugium Hypothesis (IRH), which suggests that populations contracted during interglacials and expanded in glacial times. These contrasting hypotheses are developed in the present study for the giant columnar cactus Cephalocereus columna-trajani in the intertropical Mexican drylands where the effects of Late Quaternary climatic changes on phylogeography of cacti remain largely unknown. In order to determine if the historic demography and phylogeographic structure of the species are consistent with either hypothesis, sequences of the chloroplast regions psbA-trnH and trnT-trnL from 110 individuals from 10 populations comprising the full distribution range of this species were analysed. Standard estimators of genetic diversity and structure were calculated. The historic demography was analysed using a Bayesian approach and the palaeodistribution was derived from ecological niche modelling to determine if, in the arid environments of south-central Mexico, glacial-interglacial cycles drove the genetic divergence and diversification of this species. Results reveal low but statistically significant population differentiation (FST = 0.124, P < 0.001), although very clear geographic clusters are not formed. Genetic diversity, haplotype network and Approximate Bayesian Computation (ABC) demographic analyses suggest a population expansion estimated to have taken place in the Last Interglacial (123.04 kya, 95% CI 115.3-130.03). The species palaeodistribution is consistent with the ABC analyses and indicates that the potential area of palaedistribution and climatic suitability were larger during the Last Interglacial and Holocene than in the Last Glacial Maximum. Overall, these results suggest that C. columna-trajani experienced an expansion following the warm conditions of interglacials, in accordance with the GRH.