Axially loaded tubular structures are known to be highly sensitive to initial geometric imperfections, which can significantly reduce their design bearing capacity. To address this issue, this study explores the potential of an origami-inspired design for tubular structures to achieve a lower sensitivity to imperfections. The study considers various designs, including diamond-shaped, pyramid-shaped, new Kresling, and pre-embedded rhombic origami tubes, and employs knockdown factors (KDFs) to illustrate the reduction of the design bearing capacity of these structures with initial geometric imperfections for safety purposes. Finite element analysis shows that some of the origami tubes have superior design bearing capacity, mass efficiency, and KDFs when compared to standard circular tubes. Among the origami tubes considered, the rhombic tube demonstrates the best performance and is further studied through parametric analyses of geometric design, aspect ratio, and wall thickness to achieve additional performance enhancements. Furthermore, the superior performance of the rhombic tube is evaluated and verified for various loading scenarios, including eccentric compression and compression-torsion combination. The findings of this study provide a promising approach to designing and fabricating imperfection-insensitive tubes using advanced processing technologies such as additive manufacturing. This work can potentially lead to the development of innovative tubular structures with enhanced safety and reliability in various engineering applications.