Reconfigurable structures have attracted increasing attention in numerous fields, such as aerospace, biomechanical, and civil engineering, owing to their nature to reshape and readjust without altering their original architectures. However, one of the most challenging issues in designing a reconfigurable structure is to ensure a load-bearing capacity after reconfiguration, while keeping the structural flexibility during the transformation process. Here, an origami tube that can be easily reconfigured into multiple shapes, yet offering a stiffening mechanism for load-bearing purposes is presented. A complete set of possible configurations that a single design can be reconfigured into is mathematically identified and classified. Significant differences in their axial stiffness for various configurations are analytically and experimentally investigated. Lastly, a self-reconfiguring and stiffening mechanism of the proposed origami tube structure made with shape memory polymer (SMP), which automatically reinforces its axial stiffness about an order of magnitude through kinematic transitions is demonstrated.