As older adults age, changes in their physiological, psychological, and cognitive functions often lead to inherent anxiety and fear regarding the use of digital technologies. Cognitive age, reflecting an older adult’s mental perception of their chronological age, is a crucial moderating factor in shaping their willingness and behavior towards technology adoption. However, the mechanisms through which cognitive age impacts the behavior of older adults within the realm of digital technology utilization remain unclear. Thus, grounded in the Extended Technology Acceptance Model (ETAM) and employing structural equation modeling, this study intends to investigate mechanisms which influence older adults’ behavioral intentions towards the use of museum digital displays. Consequently, it confirms that attitudes mediate the correlation between perceived usefulness, subjective norm, perceived self-efficacy, and the behavioral intention towards museum digital display utilization. Perceived ease of use does not directly affect attitudes, but instead exerts an indirect impact on attitude through perceived usefulness. Cognitive age negatively moderates the relationship between attitudes and the behavioral intention to use digital technologies. Additionally, the mediating role of attitudes in the correlation between older adults’ perception of museum digital displays and behavioral intention is moderated by cognitive age. Specifically, older adults with a higher cognitive age value (who perceive themselves to be younger than their chronological age) exhibit a weaker mediating effect of attitudes on the relationship between perceived usefulness and behavioral intention compared to those with a lower cognitive age value (who perceive themselves to be older than their chronological age). The findings seek to unbox the “black box” of how cognitive age mediates the correlation between attitudes and behavioral intention towards the use of museum digital displays among older adults, providing valuable theoretical insights for the bidirectional enhancement of digital technology utilization, the overall well-being of older adults, and high-quality development in museums.