Aiming at the issue of poor stability of visual localization and mapping (SLAM) methods during dynamic low-altitude flight of unmanned aerial vehicles (UAVs) in the absence of navigation signals, this paper proposes a UAV visual localization method based on edge features, which generates the edge features by downsizing the traditional feature extraction algorithm and finally completes the position estimation by nonlinear optimization. A convolutional neural network is employed to match edge features between consecutive key frames, yielding an edge feature reprojection error function, and finally the position estimation is completed by nonlinear optimization. The experimental results demonstrate that compared to the state-of-the-art ORB-SLAM3 algorithm, the proposed method reduces localization time by 31% on the dataset and improves localization accuracy by 15.04% in low-texture scenes. Flight experiments further indicate a significant enhancement in the accuracy and stability of UAV localization.