Manual rigid endoscopes have defects such as a low efficiency, difficult operation, and safety risks, and the antinoise interference ability, convergence speed, and control accuracy of the neural network control technology for the existing autonomous endoscopes are often ignored. Solving these problems is important for the stable operation of endoscopes. Therefore, a new adaptive fast convergent antinoise dual neural network (AFA-DNN) controller for the visual servo control of ten-degree of freedom flexible endoscope robots (FERs) with physical constraints is proposed in this work. First, the control scheme of the FERs is formulated as a quadratic programming problem, and then, an AFA-DNN visual servo controller is designed for the FERs. The adaptive gains of the controller can accelerate the convergence, improve the antinoise ability, and increase the convergence accuracy of the controller. Then, according to the Lyapunov theory, the fast convergence of the AFA-DNN in finite time is proven for both noise-free and noisy conditions. The experimental results indicate that the FER controlled by the proposed AFA-DNN can accurately track various trajectories and that the AFA-DNN has a better antinoise interference ability, higher convergence accuracy, and faster convergence speed than conventional methods. The convergence speed of the AFA-DNN is increased by a factor of 4.22 by using the adaptive gains. Experiments also indicate that the AFA-DNN remains well functioning under various noise disturbances (such as constant, periodic, linear, and Gaussian noise).