Underwater stereo cameras can effectively capture intricate environments with restricted accessibility, offering an appealing solution for precise perception. Stereo imaging is however susceptible to distortions caused by the refraction of incoming rays. These distortions are nonlinear and challenge the standard single viewpoint projection assumption. In this paper, we propose a data-driven implicit calibration method for underwater stereo cameras. To address the imaging characteristics and aberration distributions across different coordinates of underwater stereo cameras, we have developed the corresponding coordinates regression network and fusion strategy, thereby converting the calibration process into network-based learning. Secondly, we designed an underwater self-luminous calibration target system and the underwater corner point extraction strategy for sample dataset acquisition. We evaluated the proposed method comprehensively in terms of measurement, camera posture estimation, and 3D reconstruction, and compared it with other explicit calibration methods. The experimental results show that the proposed implicit calibration method is superior to other explicit calibration. We demonstrate with real experiments that our method enables efficient camera calibration for underwater vision applications.