This paper presents a computationally efficient approach that can be applied to visual simultaneous localization and mapping (SLAM) for the autonomous inspection of underwater structures using monocular vision. A selective image registration scheme consisting of key-frame selection and key-pair selection is proposed to effectively use visual features that may not be evenly distributed on the surface of underwater structures. The computational cost of the visual SLAM algorithm can be substantially reduced using only potentially effective images and image pairs by applying the proposed image registration scheme. The performance of the proposed approach is demonstrated on two different experimental datasets obtained using autonomous underwater vehicles.