As the population worldwide continues to age and the percentage of elderly people continues to increase, falls have been become the second leading cause of death from accidental or unintentional injuries. Although many imaging sensing devices have been used to detect falls for elderly people, most involve using the Internet to transfer images taken by a camera to a large back-end server, which performs the necessary calculations; however, algorithm limitations and computational complexity may cause bottlenecks in image outflow, and the image transfer can result in privacy problems. To address these problems, in this paper, an artificial intelligence (AI) fall detection method is proposed that operates using an edge computing architecture, called the pose estimation-based fall detection methodology (PEFDM), which is based on a human body posture recognition technique. The proposed PEFDM can effectively reduce the computational load, runs smoothly on mainstream edge computing systems and possesses artificial intelligence computing capabilities. By using edge computing, the privacy and upload bandwidth issues caused by image outflow can be eliminated. Experiments with real humans show that the PEFDM can detect falls for elderly people with a recognition accuracy of up to 98.1%.