In response to the limited robustness caused by the narrow field-of-view of traditional cameras and the constraints imposed by image distortion in existing panoramic Simultaneous Localization and Mapping (SLAM) algorithms, this study proposes a novel panoramic visual SLAM technology based on spherical mapping. By constructing a spherical grid using Goldberg polyhedra, the mapping relationship between pixels in panoramic two-dimensional images and spherical pixels is established, enabling feature extraction and matching on the spherical grid. Pose estimation is constrained by the polar curve equation, which facilitates the determination of three-dimensional point coordinates. Moreover, the Jacobian matrix of the optimization variables is derived to realize panoramic SLAM. This method fully exploits the geometric characteristics of panoramic cameras, effectively extracts information from panoramic images, and mitigates the effects of distortion. Experimental results demonstrate that the proposed algorithm enhances the capability of extracting information from panoramic image features, increases the quantity and accuracy of feature matches, and ensures the SLAM algorithm′s trajectory accuracy. Compared to the existing OpenvSLAM algorithm, the proposed method achieves higher localization precision and stability.