Accurate localization of moving sensors is essential for many fields, such as robot navigation and urban mapping. In this paper, we present a framework for GPS-supported visual Simultaneous Localization and Mapping with Bundle Adjustment (BA-SLAM) using a rigorous sensor model in a panoramic camera. The rigorous model does not cause system errors, thus representing an improvement over the widely used ideal sensor model. The proposed SLAM does not require additional restrictions, such as loop closing, or additional sensors, such as expensive inertial measurement units. In this paper, the problems of the ideal sensor model for a panoramic camera are analysed, and a rigorous sensor model is established. GPS data are then introduced for global optimization and georeferencing. Using the rigorous sensor model with the geometric observation equations of BA, a GPS-supported BA-SLAM approach that combines ray observations and GPS observations is then established. Finally, our method is applied to a set of vehicle-borne panoramic images captured from a campus environment, and several ground control points (GCP) are used to check the localization accuracy. The results demonstrated that our method can reach an accuracy of several centimetres.