In this paper，a bistable piezoelectric vibration energy harvester is proposed to harvest vibration energy effectively for wideband random weak excitations. Different from the classical bistable harvesters，this configuration’s bi-stability is realized by the motion of inertial mass. Under the vibration excitations，the inertial force produced by the inertial mass can be amplified and acts on two piezoelectric beams，driving the system to execute snap-through motions easily and generating large outputs. The electromechanical coupling model is established，and corresponding nonlinear dynamical equations are derived. The output characteristics of the system are studied through simulation. The results show that the harvester could realize snap-through motion under weak excitation in a wide frequency range. The length of linkage could have great influence on the shape of the system potential energy.The prototype of the harvester is fabricated and the experimental study is carried out. The sweeping frequency experiments show that the increase of inertial mass can significantly shift the start working frequency to the low frequency. The harvester can realize jumping between two potential wells for a wide range of excitation frequency. It could produce large output voltages. The experimental results for random excitations show that the harvester could execute snap-through motion under weak excitations，which prove the predictions of theoretical analysis.