Interventional surgery robots are essential in cardiovascular surgery as remote medical devices. By performing remote surgery, surgeons can reduce surgical fatigue and after-effects from heavy surgical instruments and radiation, ensuring that cardiovascular surgery is performed in a safe and reliable manner. To enhance stability during interventional procedures and reduce the impact of surgical risk due to factors where the robotic guidewire section from the end is vulnerable to mechanical jitter or blockage by blood flow, lipids, and thrombus inside the vessel, a new control method is proposed. The active disturbance rejection controller (ADRC) combined with intelligence algorithms is used to improve the performance of the controller by introducing the fuzzy inference algorithm and RBF neural network algorithm to self-adjust the parameters of the controller so that it has a greater ability to compensate for the disturbance factors appearing in the system. In numerical simulation experiments, the advantages and disadvantages of the ADRC combined with intelligence algorithms and the control performance of the conventional control strategy are analyzed in terms of the following: disturbance suppression performance and flexibility performance, respectively. Finally, different types of working conditions have been designed in the experimental platform to simulate the operation flow of in vivo vascular surgery. Experimental results show that the controller proposed in this paper meets the high accuracy, fast response, and low deviation required by interventional vascular surgery robots in complex surgical environments and can provide a more reliable guarantee for the stability of interventional surgery robots.