In order to realize the multi-modal motion of continuum robotic arm and solve the problem that the existing robotic arm can only achieve single bending or rotation, a single-module multi-degree-of-freedom flexible continuum robotic arm based on rolling contact is designed. The rolling contact module was used as the skeleton structure of the bending module in the continuum robotic arm, and the rotating module was installed in the bending module to form a multi-degree-of-freedom robotic arm with independent bending and rotation motions. The kinematics model of the continuum robotic arm was established by the segmented constant curvature method, and its stiffness, bending and rotation properties were analyzed. A continuum robotic arm prototype was prepared, and experiments were carried out on the robotic arm to unscrew bottle caps, switch on the fan, and grasp the object by avoiding obstacles in the three-dimensional space. The experimental results showed that different tasks in complex spatial environment could be accomplished by the combined motion of bending and rotation, which reflected the advantages of the composite motion mode. The designed continuum robotic arm has multi-modal motion, which provides a new idea for the design of multi-degree-of-freedom continuum robotic arms and expands the application scenarios of continuum robotic arms.