To solve the problems of existing swallowing robots, such as low load capacity, small deploy/fold ratio, and small swallowing space, this article presents a new snake-inspired swallowing robot (SSR) that can synchronously deploy and fold both axially and radially. The SSR is composed of multiple modules, each of which includes two end disk mechanisms (EDMs) and three connecting backbone mechanisms (CBBMs). The EDM is designed based on Hoberman’s linkages to achieve a radial deployment and a folding motion, while the CBBM is designed to realize the axial deployment and the folding movement and connect the EDMs. In addition, the driving device is designed. Then, to achieve the maximum deploy/fold ratio of the SSR and meet the requirements of assembly, the length of the rods is optimized on the basis of the kinematics analysis of the SSR. The final deploy/fold ratio reached up to 2.2459. The ratio of the maximum to the minimum swallowing space is 28.2754. In the end, experiments are conducted to evaluate the ability to swallow and store one object and multiple objects.