3D reconstruction plays an increasingly important role in modern photogrammetric systems. Conventional satellite or aerial-based remote sensing (RS) platforms can provide the necessary data sources for the 3D reconstruction of large-scale landforms and cities. Even with low-altitude UAVs (Unmanned Aerial Vehicles), 3D reconstruction in complicated situations, such as urban canyons and indoor scenes, is challenging due to the frequent tracking failures between camera frames and high data collection costs. Recently, spherical images have been extensively exploited due to the capability of recording surrounding environments from one camera exposure. Classical 3D reconstruction pipelines, however, cannot be used for spherical images. Besides, there exist few software packages for 3D reconstruction of spherical images. Based on the imaging geometry of spherical cameras, this study investigates the algorithms for the relative orientation using spherical correspondences, absolute orientation using 3D correspondences between scene and spherical points, and the cost functions for BA (bundle adjustment) optimization. In addition, an incremental SfM (Structure from Motion) workflow has been proposed for spherical images using the above-mentioned algorithms. The proposed solution is finally verified by using three spherical datasets captured by both consumer-grade and professional spherical cameras. The results demonstrate that the proposed SfM workflow can achieve the successful 3D reconstruction of complex scenes and provide useful clues for the implementation in open-source software packages. The source code of the designed SfM workflow would be made publicly available.