Abstract: A new configuration of a 6-degree-of-freedom continuum robot for single-port surgery is proposed. The deformable skeleton of the robot is made from the super-elastic nickel-titanium materials and manufactured by integrated processing technology, and has a series of elastic joints with cross-cut notches. The kinematics model is established and the reachable workspace is analyzed for the robot. An optimized search method for the surgical operation workspace is proposed to analyze the operational dexterity at key points in the workspace. Furthermore, a parameter optimization method for improving the operational dexterity of the continuum robot for single-port surgery is proposed. With the operational dexterity at key points as the objective and the joint deformability as the constraint, the geometric parameters of the deformable skeleton of the continuum robot are optimized. Finally, the motion control experiment of the continuum robot is carried out. The distal end position error of the robot is 2.23 mm and angle error is 2.06°, which verifies the accuracy of the model.