Directly monitoring abundance of cryptic species, such as mountain lions (Puma concolor), over large areas is a challenge for wildlife managers because traditional population estimation techniques may be impractical and expensive. We generated annual estimates of mountain lion abundance in Arizona, USA, for 2004–2018 by employing statistical population reconstruction methods, which use available age‐at‐harvest data and auxiliary information such as estimated survival rates, harvest probabilities, and hunter effort. Using PopRecon 2.0 software, we estimated that the statewide abundance of all mountain lions including kittens ranged from 1,848 (95% CI = 650–3,046) to 4,661 (95% CI = 393–9,030) during 2004–2018. Abundance for subadults and adults was more stable and precisely estimated, ranging from 1,166 (95% CI = 622–1,709) to 1,715 (95% CI = 872–2,558). Our results suggest a stable statewide mountain lion population. This approach provides a practical and cost‐effective option for monitoring Arizona's mountain lion population, and will improve the ability of managers to monitor the population annually to respond to changes in abundance and to evaluate factors that influence mountain lion abundance. © 2019 The Authors. Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.