Origami structures, which were inspired by traditional paper folding arts, have been applied for engineering problems for the last two decades. Origami-based thin-wall tubes have been extensively investigated under axial loadings. However, less has been done with radial stiffness as one of the critical mechanical properties of a tubular structure working under lateral loadings. In this study, the radial stiffness of novel thin-wall tubular structures based on origami patterns have been studied with compression tests and finite element analysis (FEA) simulations. The results show that the radial stiffness of an origami-inspired tube can achieve about 27.1 times that of a circular tube with the same circumcircle diameter (100 mm), height (60 mm), and wall thickness (2 mm). Yoshimura, Kresling, and modified Yoshimura patterns are selected as the basic frames, upon which the influences of different design parameters are tested and discussed. Given that the weight can vary due to different designs, the stiffness-to-weight ratio is also calculated. The origami-inspired tubular structures with superior stiffness performances are obtained and can be extended to crashworthy structures, functional structures, and stiffness enhancement with low structural weight.