Magnetoelectric (ME) transducers were originally intended for magnetic field sensors but have recently been used in vibration energy harvesting. In this paper, a new broadband vibration energy harvester has been designed and fabricated to be efficiently applicable over a range of source frequencies, which consists of two cantilever beams, two magnetoelectric (ME) transducers and a magnetic circuit. The effects of the structure parameters, such as the non-linear magnetic forces of the ME transducers and the magnetic field distribution of the magnetic circuit, are analyzed for achieving the optimal vibration energy harvesting performances. A prototype is fabricated and tested, and the experimental results on the performances show that the harvester has bandwidths of 5.6 Hz, and a maximum power of 0.25 mW under an acceleration of 0.2 g (with g = $9.8;ms^2$).