Robot-assisted systems have been developed for minimally invasive surgical procedures, which bring tremendous benefits for patients, such as less trauma, less bleeding, and shorter recovery time. Among the contemporary surgical robotic manipulators, flexible serpentine manipulator shows great advantages on operating with complicated nonlinear anatomical constraints, and it can reach deep occluded surgical targets without colliding in a critical anatomical environment. In surgical robotic operation, less spatial sweeping area from the flexible manipulator in motions is desired to induce the minimal surgical complications. The goal of our research is to reduce unnecessary sweeping motion of the flexible surgical manipulator in operations, and to obtain safer and more reliable reference trajectories. A novel 3-D neural dynamic model is proposed and expected to obtain the safety-enhanced trajectory in workspace with the consideration of minimum sweeping area. In this model, the neural stimulation propagates from the start state to the whole network through the connective weight of manipulator’s sweeping area. According to the results of comparative studies with commonly used planning algorithms in various simulation scenarios, the proposed planning algorithm is validated in terms of effectiveness and safety. Ultimately, the experiments on phantoms and preclinical cadaveric human head show the feasibility of the proposed safety-enhanced planning algorithm.