Currently, internet services are developing rapidly, and the relationship between specific types of internet services and the well-being of older adults is still unclear. This study took a total of 353 urban older adults aged 60 years and above as research objects to explore the impact of the use behavior toward internet-based medical services (IBMS) on their well-being through an online questionnaire. This study integrated well-being theory and peer support theory, constructed an extended structural equation model of technology acceptance based on the technology acceptance model (TAM), and analyzed the variable path relationship. The results confirm the proposed model: older adults improved their eudaimonic well-being through using IBMS; perceived usefulness significantly affected the older adults’ attitudes towards IBMS; perceived ease of use significantly affected the use of IBMS through mediation; peer support significantly affected older adults’ attitudes, willingness, actual use, and well-being in the process. This study proposes that facilitating IBMS use for older adults in the development and design of internet technology programs should be considered in order to provide them with benefits. Moreover, paying attention to peer support among older adults plays an important role in the acceptance of new technologies and improving their well-being. The “peer support” of this study expanded and contributed to the research on the impact on older adults’ well-being and the construction of a technology acceptance model. The peer support in this study extended the influence factor of eudaimonic well-being and contributed to the further development of the TAM.