Tendon-driven continuum robots (TDCRs) have infinite degrees of freedom and high flexibility, posing challenges for accurate modeling and autonomous control, especially in confined environments. This paper presents a model-less optimal visual control (MLOVC) method using neurodynamic optimization to enable autonomous target tracking of TDCRs in confined environments. The TDCR’s kinematics are estimated online from sensory data, establishing a connection between the actuator input and visual features. An optimal visual servoing method based on quadratic programming (QP) is developed to ensure precise target tracking without violating the robot’s physical constraints. An inverse-free recurrent neural network (RNN)-based neurodynamic optimization method is designed to solve the complex QP problem. Comparative simulations and experiments demonstrate that the proposed method outperforms existing methods in target tracking accuracy and computational efficiency. The RNN-based controller successfully achieves target tracking within constraints in confined environments.