Furcraea parmentieri (Roezl ex Ortgies) García‐Mend. is a long‐lived, semelparous threatened species with a restricted geographic distribution. We studied the demography of this species in southwest of Mexico City using periodic matrices. We followed the fate of 404 individuals (in 2006–2007) and performed seed germination and seedling establishment experiments in the field (in 2007–2008) to estimate survival, growth and reproduction probabilities of individuals in eight size categories, according to plant height. Population structure was characterized by a high number of saplings, as well as medium and large plants. We built three annual matrices that described the demography in different phases of the population cycle: regular years (RG) characterized by low fecundity and low adult mortality; mast‐seeding years (MS) with low seedling emergence and high adult mortality (related to semelparity); and post mast‐seeding years (PS) with a high emergence of seedlings and bulbils. Periodic matrices were built simulating three scenarios, which consisted of mast‐seeding events occurring every 5, 10, or 15 years. Finite population growth rates (λ) were 1.03 (RG year), 0.99 (MS year), and 1.25 (PS year). The long term population growth rate values projected over a 90 year period (estimated on an annual basis) were higher as the frequency of mast‐seeding events increased. We estimated that individuals reproduce at an age of 60–90 years and that most new recruits originate via sexual reproduction. Although the population has a potential for growth, its persistence may be threatened due to land use change.