Continuum robots are suitable for operating in unstructured environments owing to their intrinsic compliance. This paper presents a novel tendon-driven continuum robot equipped with two modules and a compliant backbone formed by helical springs. Each module is driven by four parallel arranged tendons to implement a redundant actuation system that guarantees dexterous motions of the robot. A position feedback controller for the continuum robot is then developed, and a quadratic programming algorithm is incorporated into the controller to achieve a smooth configuration of the robot. Experiments results show that the control method has good trajectory tracking performance against external disturbances.