Continuum robots have attracted increasing attention in recent years due to their intrinsic compliance and safety. Nevertheless, the use of structure compliance may lead to reduction of stiffness and positioning precision. This paper presents a novel design of a hybrid continuum robot whose actuators are composed of pneumatic muscles and embedded elastic rods. Such robot can switch drive modes between large-scale movement and fine adjustment of position by employing a locking mechanism to change its stiffness. A three-dimensional static model of the robot is presented using an improved Kirchhoff rod theory, where elastic deformation of the robot is accounted for from an optimal control point of view via minimal total potential energy principle. Experiments were carried out to validate the static model and to test the stiffness and precision of the robot. This work provides a possible way to strengthen the control precision of a continuum robot with compliant structure.