Vibration energy harvesting converts mechanical energy from ambient sources to electricity to power remote sensors. Compared to linear resonators that have poor performance away from their natural frequency, nonlinear vibration energy harvesters perform better because they use vibration energy over a broader spectrum. We present a hybrid nonlinear energy harvester that combines bi-stability with internal resonance to increase the frequency bandwidth. A two-fold increase in the frequency bandwidth can be obtained compared to a bi-stable system with fixed magnets. The harvester consists of a piezoelectric cantilever beam carrying a movable magnet facing a fixed magnet. A spring allows the magnet to move along the beam and it provides an extra stored energy to further increase the amplitude of vibration acting as a mechanical amplifier. An electromechanically coupled mathematical model of the system is presented to obtain the dynamic response of the cantilever beam, the movable magnet and the output voltage. The perturbation method of multiple scales is applied to solve these equations and obtain approximate analytical solutions. The effects of various system parameters on the frequency responses are investigated. The numerical approaches of the long time integration (Runge-Kutta method) and the shooting technique are used to verify the analytical results. The results of this study can be used to improve efficiency in converting wasted mechanical vibration to useful electrical energy by broadening the frequency bandwidth. (C) 2016 Elsevier Ltd. All rights reserved.