This article presents a monocular-based navigation approach for unmanned aerial vehicle safe and continuous inspection along one side of transmission lines. To this end, a navigation model based on the transmission tower and the transmission-line vanishing point was proposed, and the following three key issues were addressed. First, a deep-learningbased object detection and a fast and smooth tracking algorithm based on the kernelized correlation filter were combined to locate transmission tower timely and reliably. Second, the vanishing point of transmission lines was computed and optimized to provide unmanned aerial vehicle with a robust and precise flight direction. Third, to keep a stable safe distance from transmission lines, the transmission lines were first rectified by optimizing a homography matrix to eliminate the parallel distortion, and then their interval variation was estimated for reflecting the spatial distance variation. Finally, the real distance from transmission tower was measured by the triangulation across multiple views. The proposed navigation approach and the designed UAV platform were tested in a field environment, which achieved an encouraging result. To the best of authors' knowledge, this article marks the first time that a safe and continuous navigation approach along one side of transmission lines is put forward and implemented.