Miura-ori pattern was adopted to form the tessellation design of slender braces to improve the energy dissipation capacity under the low-cycle repeated loading. The energy dissipation mechanisms of origami energy dissipation braces (OEDBs) and conventional square braces with equal bearing capacity were compared. Finite element models for hysteretic simulation were constructed and analyzed to figure out the influences of various geometrical design parameters on the hysteretic behavior of OEDBs. The results show that the OEDBs have an obvious improvement in the energy dissipation capacity compared to conventional square braces. The influence of parameters on energy dissipation capacity is quite different. The smaller folding angles, smaller aspect ratios, and larger width-to-thickness ratio play positive roles in improving energy dissipation performance rather than elastic stiffness. However, smaller slenderness improves both while the change of in-plane angle is sensitive to the hysteretic performance.