This study employed a new method (nonlinear method) called back-propagation network [BPN] to analyze the adoption model of telecare. It is important to inform professionals of the need for medical statistics knowledge to better evaluate new technologies, particularly in health technologies assessment agencies. This study used face-to-face interviews to collect senior citizens aged over 60 years in Taiwan, and it used BPN based on the technology acceptance model to identify a telecare adoption model. Lastly, this study compared traditional methods and the BPN method. The BPN method is much better than traditional method. Moreover, the main research result showed that people's perceived usefulness must be raised to effectively increase the adoption of telecare. Education and training for ease of use of telecare for users appear especially important. In sum, this research recommends making the operation interfaces of telecare more user-friendly and providing a demonstration system for practice, so that users would be more comfortable using the system. The findings of this research suggest that, to develop training for users to use telecare, it is likely to be helpful to reduce users' anxiety and improve usage of telecare. The utilization of the adoption model of telecare established by the BPN method of artificial neural networks is feasible. These findings may offer significant reference for subsequent studies.