Power Internet of things (PIoT) is an important infrastructure to support the construction of smart grid. Remote areas such as grasslands and Gobi are important export places of power energy, and a large number of PIoT devices are scattered in these areas. The traditional terrestrial 5G network has high construction cost and relatively concentrated computing resources, which is not suitable for serving delay-sensitive and computationally complex intelligent PIoT tasks in remote areas. The satellite-terrestrial integrated network (STIN) and cloud-edge collaborative scheme for 6G provide a good idea to solve the above problems. In this paper, a 6G-oriented satellite-terrestrial cooperative integrated power IoT is constructed, which aims to support the Internet access of widely distributed PIoT devices in remote areas. A cloud-edge collaborative computing mode is proposed to meet the delay constraints and computational requirements of various artificial intelligence applications in the PIoT. In order to minimize the completion time cost of tasks, we formulate the optimization problem, and solve the optimal task offloading scheme by greedy algorithm. The experimental results show that the cloud-edge collaborative computing model shows good delay advantages and computing performance in the satellite-terrestrial integrated power Internet of things architecture.