In order to meet the operational needs in some narrow environments, the hyper-redundant snake-shaped manipulator has received extensive attention and has been widely studied due to its compact shape and multiple degrees of freedom. At present, the research of hyper-redundant manipulator mainly focuses on the straight push platform. Considering the limitation of working space, this paper designed a hyper-redundant manipulator delivered by a curled turntable. According to the characteristics of turntable delivery, a tip-following algorithm based on curve fitting and a tip-following strategy based on terminal posture record are proposed. Finally, with the algorithm applied to the physical robot we made, we successfully realized the tip-following motion control of the hyper-redundant manipulator.