Optical coherence tomography (OCT) plays a crucial role in diagnosing corneal diseases due to its capacity to provide high-resolution three-dimensional imaging. However, the convex shape of the cornea and the inherent trade-off between depth of field (DOF) and lateral resolution in OCT systems often result in defocusing issues, leading to reduced lateral resolution and sensitivity in single-shot high-resolution imaging. Traditional methods typically involve multiple focusing at different depths followed by image stitching to achieve full-depth high-resolution imaging of the cornea, which increases imaging times and introduces potential stitching artifacts. To address these limitations, we propose a novel adaptive focusing OCT system. By leveraging the symmetry of the corneal structure and the periodic focusing stability of an electrically tunable lens, our system can achieve full-depth high-resolution imaging of the entire cornea in a single scan, covering an 11 mm imaging range and 1.5 mm depth variation with a lateral resolution of 10 µm. This approach not only halves the imaging time but also eliminates the need for image stitching. Imaging of curved tape samples and excised porcine corneas demonstrates the potential of this novel technique for high-resolution and fast corneal imaging.