To enable real-time adjustments of laser beam pointing in satellite laser ranging systems with bistatic units, this study proposes a method for real-time recognition of laser beam pointing key points using a deep learning model. By collecting and labeling numerous successful satellite observation laser beam images and applying data augmentation, this paper establishes a comprehensive laser beam pointing image dataset. The YOLOv8-Pose deep learning algorithm is utilized for model training, and ultimately applying the model to satellite laser observations. Compared with traditional edge extraction methods for laser beam images, the proposed algorithm demonstrates excellent adaptability, achieving an impressive mean average precision of 99.39%. In addition, the proposed algorithm addresses the challenge of accurately recognizing laser beam pointing key points in relatively poor weather conditions, paving the way for an automated satellite laser ranging system.