Wake galloping energy harvesting have been extensively developed to scavenge flow energy from vortex-induced oscillations. Hence, the wake-galloping harvester only has a natural frequency which leads to a very narrow bandwidth. Therefore, it does not operate well under the wide region of shedding frequencies in variable wind speed. To overcome the vital issue, this paper we explored a novel two-degree-of-freedom nonlinear flow energy harvester to collect flow energy induced by the wake of a bluff body. The nonlinear restoring force is realized by using a repulsive magnetic force between two cuboid-shaped permanent magnets, and the electromechanical coupling equations is presented. Based on the method of harmonic balance, the electromechanical governing equations is decoupled, and the first order harmonic solutions are implemented. The modulation equations are established, the amplitude-frequency figures of displacement and voltage are depicted with different detuning parameters. The superiority of the presented energy harvester is contrasted with the single-degree-of-freedom linear and nonlinear cases, the results revealed that the two-degree-of-freedom nonlinear scheme can enhance the bandwidth of flow energy capture. The effect of physical parameters on the scavenged power is discussed. The accuracy and efficiency of the approximate analytical data are examined by numerical simulations.