In this paper, the nonlinear governing equation is firstly established for an energy harvester with bistable buckled beam. The nonlinear vibration response is studied using Galerkin method and the method of multiple scales. The frequencyresponse curves are depicted to examine the influence of excitation frequency and external excitation amplitude on the structural vibration characteristics. Based on energy analysis method (Hamilton′s principle, Galerkin discretization, etc.), the nonlinear dynamics of the structure are investigated for the case of internal resonance with a ratio of 1 to 2. The numerical results show that periodic motions and chaotic motions occur in this structure system.