An endoscope holder must understand the detailed surgical actions and the surgeons’ visual attention to keep important targets in the field of endoscopic view during operations. From an intensive analysis of the surgeons’ attention mechanism, we included that surgical actions, like cutting, suturing, etc., play an important role in determining the positions and weights of visual attention points during a dynamic surgical scene. To perform this process, this work proposes a Surgical Action-driven Visual Attention network (SAVAnet) and applies the network in autonomous endoscope control. Four scenarios are constructed in the da Vinci V-rep simulator: pick&place and needle exercise in a general laparoscopic training environment, needle driving with and without obstacle removal in an abdominal cavity, to create datasets for network training. The results show that the network has an outstanding performance in surgical action prediction with a high average accuracy of over 91%. Additionally, with surgical action guidance, the attention point prediction has higher accuracy and accords with surgeons’ visual attention. Finally, the acquired attention points are utilized to execute visual servoing in simulation. The results verify that the SAVAnet is feasible for autonomous endoscope control in real-time and lays a theoretical foundation for future sim-to-real execution. Note to Practitioners—This paper was motivated by the problem of endowing an endoscope with surgeons’ visual attention mechanism, which is affected by surgical actions, for autonomous endoscope control. An eye-tracking device has been utilized to detect surgeon’s visual attention in real-time and then control the endoscope to follow what the surgeon is looking at. However, this approach is susceptible to the surgical environment. Besides, many instrument detection and segmentation algorithms are developed for automatic surgical instrument tracking. However, surgeons’ visual attention does not always focus on the instruments during operations. In this work, we propose a novel SAVAnet to determine visual attention based on surgical actions. We prove from many qualitative and quantitative experiments that surgical actions play a significant role in determining visual attention. The designed SAVAnet can predict surgical actions correctly and then effectively guide the choice of visual attention. Finally, the simulation results show that the SAVAnet can endow endoscope with surgeons’ visual attention to perform self-control in real time. In future research, we will train the SAVAnet using real datasets and conduct more physical experiments on real surgical robots.