Industrial Internet of unmanned aerial vehicles (IIoUAVs) that enable autonomous inspection and measurement of anything anytime anywhere have become an essential component of the future industrial Internet of things (IIoT) ecosystem. In this paper, we investigate how to apply IIoUAVs for power line inspection in smart grid from an energy-efficiency perspective. First, the energy consumption minimization problem is formulated as a joint optimization problem, which involves both the large-timescale optimization, such as trajectory scheduling, velocity control, and frequency regulation, and the small-timescale optimization, such as relay selection and power allocation. Then, the original NP-hard problem is transformed into a two-stage suboptimal problem by exploring the timescale difference and the energy magnitude difference between the large-timescale and the small-timescale optimizations, and is solved by combining dynamic programming (DP), auction theory, and matching theory. Finally, the proposed algorithm is verified based on real-world map and realistic power grid topology.