Continuum robots are flexible and compliant. Compared to the case in conventional articulated manipulators, the driving unit can be placed outside the workspace of the robot, so that the motion orientation has a relatively complete linear configuration flow, which can be applied to a special environment with narrow and multiple obstacles such as aerospace. This study presents the development process of a tendon-driven continuum robot (TCR) with a high length-diameter ratio. The skeleton structure which imitates a snake is composed of continuous joints in series. The driving device is operated by using a tendon-driven method, which reduces the complexity of the driving box and control system significantly. The diameter of the robot is designed to be 5 mm, which enables it to work in a narrow and slender space with certain flexibility. Subsequently, a kinematic model of the robot is established. The mode function backbone method is applied to realize TCR trajectory planning. An idea of segmented solving is adopted to achieve trajectory tracking control of the continuum robot. Finally, a prototype of the continuum robot is produced, and the rationality of the robot design and the effectiveness of the motion control method are verified through trajectory simulations and experiments. The robot can perform inspection tasks within a narrow gap of 20 mm with good environmental adaptability.