With the gradual commercialization of 5G, especially the widespread application of artificial intelligence (AI) technology, the Internet of Things (IoT) continues to expand and has integrated into every aspect of our lives. While enjoying the convenience brought by IoT, we also face unprecedented challenges, including ubiquitous and unpredictable demands for communication and computing resources. In consideration of their flexible deployment, low cost, and easy expansion, UAV edge computing IoT networks (UECINs), which adopt unmanned aerial vehicles (UAVs) to provide fast communication and computing services, have emerged as a promising solution. Note that there have been a number of studies focusing on UAV’s position deployment and trajectory design, resource allocation in UECIN. However, most existing works proposed short-term service provisioning systems with a fixed number of UAVs, ignoring the problem of UAVs’ limited battery power and the possible changes of ground users’ number, locations, and resource requirements. To address these issues, we present a dynamic UECIN framework with autonomous prediction characteristics, aiming to stably provide mobile-edge computing services for ground users in a certain area over a long period of time. This framework can not only support UAV’s dynamic entry and exit according to the real-time needs of ground users but also update their position deployment based on the distribution of ground users. As we know, we are the first to propose UECIN with a dynamic entry and exit mechanism. Besides, an efficient and load-balancing task allocation scheme is further given, and extensive analysis and numerical results corroborate the feasibility and superior performance of our framework.