The advantages of a cloud computing service are cost advantages, availability, scalability, flexibility, reduced time to market, and dynamic access to computing resources. Enterprises can improve the successful adoption rate of cloud computing services if they understand the critical factors. To find critical factors, this study first reviewed the literature and established a three-layer hierarchical factor table for adopting a cloud computing service based on the Technology-Organization-Environment framework. Then, a hybrid method that combines two multi-criteria decision-making tools-called the Fuzzy Analytic Network Process method and the concept of VlseKriterijumska Optimizacija I Kompromisno Resenje acceptable advantage-was used to objectively identify critical factors for the adoption of a cloud computing service, replacing the subjective decision of the authors. The results of this study determined five critical factors, namely data access security, information transmission security, senior management support, fallback cloud management, and employee acceptance. Finally, the paper presents the findings and implications of the study.