Adoption of smartphones by older adults (i.e., 65+ years old) is poorly understood, especially in relation to cybersecurity and cyberthreats. In this study, we focus on the perceived threat of cyberattacks as a potential barrier to smartphone adoption and use among older adults. The study also aims at investigating the differences between users and non-users of smartphones. We conducted a quantitative cross-sectional survey of older adults in Slovenia (N = 535). The results of covariance-based structural equation modeling indicate consistent support for the associations of intention to use (ItU) with perceived usefulness (PU), subjective norm (SN) and attitude toward use (AtU), the association between ease of use (EoU) and PU, the association between hedonic motivation (HM) and AtU, and the association between smartphone technology anxiety (STA) and fear of use (FoU). Even though the negative association between perceived threat (PT) and ItU was significant in the full sample, the non-user and the not aware subsamples, its role in adoption of smartphones among older adults remains puzzling. We uncovered significant positive associations between PT and AtU (except in the not aware subsample), and PT and PU which we could not fully explain in our study. The results of our study provide some insights on how campaigns promoting adoption of smartphones among older adults, workshops, training and informal teaching might be improved.