This paper presents an operating stiffness controller (OSC) for tendon-driven continuum manipulators, designed to adjust their stiffness during minimally invasive surgery (MIS). The OSC is based on variable impedance control and Lagrangian dynamic modeling, allowing for dynamic and continuous adjustment of stiffness without altering the material or structure of the manipulator. The controller consists of a variable impedance control module and a feedback linearization module, which together enable the manipulation of stiffness by modifying driving forces along the tendons. The stability of the OSC is proven using a Lyapunov function, and its performance is evaluated through simulations and experiments. The results show that the OSC can achieve high accuracy and stability in adjusting the operating stiffness, with average errors of 7.82% and 3.09% for constant and time-varying desired stiffness, respectively. The OSC's ability to dynamically adjust stiffness makes it suitable for various stages of MIS, from the approach stage to the operation stage.This paper presents an operating stiffness controller (OSC) for tendon-driven continuum manipulators, designed to adjust their stiffness during minimally invasive surgery (MIS). The OSC is based on variable impedance control and Lagrangian dynamic modeling, allowing for dynamic and continuous adjustment of stiffness without altering the material or structure of the manipulator. The controller consists of a variable impedance control module and a feedback linearization module, which together enable the manipulation of stiffness by modifying driving forces along the tendons. The stability of the OSC is proven using a Lyapunov function, and its performance is evaluated through simulations and experiments. The results show that the OSC can achieve high accuracy and stability in adjusting the operating stiffness, with average errors of 7.82% and 3.09% for constant and time-varying desired stiffness, respectively. The OSC's ability to dynamically adjust stiffness makes it suitable for various stages of MIS, from the approach stage to the operation stage.