A mobile app could be a powerful medium for providing individual support for cognitive behavioral therapy (CBT), as well as facilitating therapy adherence. Little is known about factors that may explain the acceptance and uptake of such applications. This study, therefore, examines factors from an extended version of the Unified Theory of Acceptance and Use of Technology (UTAUT2) model to explain variation between people’s behavioral intention to use a CBT for insomnia (CBT-I) app and their use-behavior. The model includes eight aspects of behavioral intention: performance expectancy, effort expectancy, social influence, self-efficacy, trust, hedonic motivation, anxiety, and facilitating conditions, and investigates further the influence of the behavioral intention and facilitating conditions on app-usage behavior. Data were gathered from a field trial involving people (n = 89) with relatively mild insomnia using a CBT-I app. The analysis applied the Partial Least Squares-Structural Equation Modeling method. The results found that performance expectancy, effort expectancy, social influence, self-efficacy, trust, and facilitating conditions all explained part of the variation in behavioral intention, but not beyond the explanation provided by hedonic motivation, which accounted for R² = 0.61. Both behavioral intention and facilitating conditions could explain the use-behavior (R² = 0.32). We anticipate that the findings will help researchers and developers to focus on: (1) users’ positive feelings about the app as this was an indicator of their acceptance of the mobile app and usage; and (2) the availability of resources and support as this also correlated with the technology use.