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Abstract Nonhuman primates are an essential part of tropical biodiversity and play key roles in many ecosystem functions, processes, and services. However, the impact of climate variability on nonhuman primates, whether anthropogenic or otherwise, remains poorly understood. In this study, we utilized age‐structured matrix population models to assess the population viability and demographic variability of a population of geladas (Theropithecus gelada) in the Simien Mountains, Ethiopia with the aim of revealing any underlying climatic influences. Using data from 2008 to 2019 we calculated annual, time‐averaged, and stochastic population growth rates (λ) and investigated relationships between vital rate variability and monthly cumulative rainfall and mean temperature. Our results showed that under the prevailing environmental conditions, the population will increase (λ_s = 1.021). Significant effects from rainfall and/or temperature variability were widely detected across vital rates; only the first year of infant survival and the individual years of juvenile survival were definitively unaffected. Generally, the higher temperature in the hot‐dry season led to lower survival and higher fecundity, while higher rainfall in the hot‐dry season led to increased survival and fecundity. Overall, these results provide evidence of greater effects of climate variability across a wider range of vital rates than those found in previous primate demography studies. This highlights that although primates have often shown substantial resilience to the direct effects of climate change, their vulnerability may vary with habitat type and across populations.