Underwater camera calibration has attracted much attentions due to its significance in high-precision three-dimensional (3-D) pose estimation and scene reconstruction. However, most existing calibration methods focus on calibrating the underwater camera in a single scenario [e.g., air-glass-water], which can not well formulate the geometry constraint and further result in the complex calibration process. Moreover, the calibration precision of these methods is low, since multilayer transparent refractions with unknown layer orientation and distance make the task more difficult than that in air. To address these challenges, we develop a novel and efficient medium-driven method for underwater camera calibration (MedUCC), which can calibrate the underwater camera parameters, including the orientation and position of the transparent glass accurately. Our key idea of this article is to leverage the light-path changes formed by medium refractions between different media to acquire calibration data, which can better formulate the geometry constraint, and estimate the initial value of the underwater camera parameters. To improve the calibration accuracy of the underwater camera system, a quaternion-based solution is developed to refine the underwater camera parameters. To the end, we evaluate the calibration performance on an underwater camera system. Extensive experiment results demonstrate that our proposed method can obtain a better performance in comparison to the existing works. We also validate our proposed MedUCC method on our designed 3-D scanner prototype, which illustrates the superiority of our proposed calibration method.