This paper presents an electromagnetic energy harvester based on a unique nonlinear Kresling origami-inspired structure. By introducing the equilibrium shift phenomenon, reversible nonlinearity (i.e. mixed softening-hardening behavior) empowers the proposed harvester to work in a broad frequency band, confirmed by both simulation using a dynamic model and experimentation. The prototyped device can produce the open-circuit root mean square (RMS) voltage from 0.09 V to 0.20 V in the reversibly nonlinear response region in (6.19 Hz, 9.63 Hz) and a maximum output power of 0.4956 mW at an optimum load of 18.1 Ω under the excitation of 1.1 g. Moreover, detailed research further reveals that the design parameters of Kresling origami-inspired structure and electrical and mechanical loads influence reversible nonlinearity. Increasing the tip mass and γ ₀ in the M2 region of the design map strengthens the softening behavior, and enlarging the electrical load enhances the hardening behavior. The findings from this work deepen the understanding of the nonlinear behavior of Kresling origami, unveils the great potential of origami structure in energy harvesting and offers a new method to realize broadband vibration energy harvesters.