This paper proposes the design of a 360° map establishment and real-time simultaneous localization and mapping (SLAM) algorithm based on equirectangular projection. All equirectangular projection images with an aspect ratio of 2:1 are supported for input image types of the proposed system, allowing an unlimited number and arrangement of cameras. Firstly, the proposed system uses dual back-to-back fisheye cameras to capture 360° images, followed by the adoption of the perspective transformation with any yaw degree given to shrink the feature extraction area in order to reduce the computational time, as well as retain the 360° field of view. Secondly, the oriented fast and rotated brief (ORB) feature points extracted from perspective images with a GPU acceleration are used for tracking, mapping, and camera pose estimation in the system. The 360° binary map supports the functions of saving, loading, and online updating to enhance the flexibility, convenience, and stability of the 360° system. The proposed system is also implemented on an nVidia Jetson TX2 embedded platform with 1% accumulated RMS error of 250 m. The average performance of the proposed system achieves 20 frames per second (FPS) in the case with a single-fisheye camera of resolution 1024 × 768, and the system performs panoramic stitching and blending under 1416 × 708 resolution from a dual-fisheye camera at the same time.