In this paper, we propose PA-SLAM, a monocular panoramic annular visual SLAM system with loop closure and global optimization. A hybrid point selection strategy is put forward in the tracking front-end, which ensures repeatability of keypoints and enables loop closure detection based on the bag-of-words approach. Every detected loop candidate is verified geometrically and the $Sim(3)$ relative pose constraint is estimated to perform pose graph optimization and global bundle adjustment in the back-end. A comprehensive set of experiments on real-world datasets demonstrates that the hybrid point selection strategy allows reliable loop closure detection, and the accumulated error and scale drift have been significantly reduced via global optimization, enabling PA-SLAM to reach state-of-the-art accuracy while maintaining high robustness and efficiency.