Climate change is a growing threat for global biodiversity, in particular for narrow endemic species. The Mediterranean region, which harbors an exceptional biodiversity, has been identified as one of the most sensitive regions to climate change. Based on a 22-year monitoring period, we analyzed the dynamic and viability of the six extant populations of a narrow endemic plant species of the Mediterranean area, Centaurea corymbosa, to predict their fate under two climatic scenarios. We constructed matrix projection models to calculate current asymptotic growth rates and to perform stochastic projections including both demographic and environmental stochasticity. Neither asymptotic growth rates nor their temporal variance were linked to population size and age at flowering. Randomization tests showed that asymptotic growth rates were significantly different among years but not among populations. An increase in temperature and a decrease in the number of wet days had a negative impact on the whole life-cycle, particularly in the summer period, and thus reduced asymptotic growth rates. Stochastic projections showed that an increased frequency of extreme climatic events increased population extinction risk and decreased mean time to extinction. The warm scenario had a more dramatic impact on population viability than the dry scenario. Management recommendations are proposed to increase population viability of endangered plant species such as C. corymbosa that face climate change.