Snap-through oscillation has been widely utilized in nonlinear energy harvesting for power improvement and bandwidth enlargement. In this paper, the snap-through phenomenon of a bistable dual-beam vibration energy harvester (DB-VEH) when driven by harmonic and random excitations is investigated. First, the electromechanical model is established and the parameters are determined by experimental tests. Subsequently, the dynamic responses under different levels of excitation are simulated and the corresponding experiments are conducted. Results indicate that the bistable DB-VEH can achieve the inter-well and chaotic oscillations near the first and second resonances, providing two frequency bands of snap-through, which is helpful for enlarging the bandwidth. For the inter-well oscillation, the remarkably increased output of one beam is always in sacrifice of the efficiency of the other beam, resulting in an outperformed beam and an underperformed one. Finally, the performance when the bistable DB-VEH is under a random excitation is investigated in comparison with that of its linear counterpart. Results indicate that, thanks to the snap-through phenomenon, the standard deviation of voltage of a bistable DB-VEH is much higher than that of a linear DB-VEH for a certain range of intensity.