Algorithmic recommendation technology, including news apps, social networking services (SNSs), and video or short-video apps, and is widely embedded in various mobile applications (apps), has raised concerns about potential addiction. This study constructs a model linking the uses and gratifications of algorithmic recommendation apps with algorithmic dependence, with a particular focus on fatigue as a key mediator in explaining the psychological mechanism behind the formation of algorithmic app dependence. Snowball sampling was employed for data collection, and a total of 354 valid questionnaires were collected via the online survey tool (i.e., WJX platform). The results show that the use of algorithmic recommendation apps has a direct positive effect on algorithmic app dependence. While all three types of user gratification obtained (i.e., information gratification, entertainment gratification, and expression gratification) are positively related to algorithmic app dependence, the mediating role of fatigue varies: entertainment gratification indirectly reduces algorithmic app dependence by increasing fatigue, whereas expression gratification indirectly increases algorithmic app dependence by reducing fatigue. The theoretical contributions and practical implications of the research findings are discussed.