Piezoelectric effect is an effective way of harvesting energy from the environmental broadband vibration. In this paper, we investigate the coherence resonance of a piezoelectric bistable vibration energy harvester theoretically and experimentally. The device is comprised of a cantilever beam with magnetic repulsive force. Firstly, the electromechanical coupled equation is derived based on the Euler-Bernoulli beam theory. Then, analyzing the potential shapes, we learn that when the system oscillates between the two potential wells, it will produce a large voltage generally. And the beam dynamic response under the random excitation is simulated by Euler-Maruyama method. The results of simulations and experiments show that there is a coherence resonance threshold in the Duffing type piezoelectric bistable energy harvester. When the standard deviation of the random excitation is less than the threshold, the motion state of the system will be trapped in a single potential well, which results in a low average output power. And when the excitation standard deviation is larger than the threshold, the system stochastic stability will change. The dynamic displacement and strain clearly show that the system can exhibit large oscillation between the two potential wells. Then, Kramers rate is used to explain the coherence resonance threshold of the bistable system under the broadband random excitation. The experimental results show that when the coherence resonance takes place, the beam will oscillate between the two potential wells more frequently, and the broadband vibration energy can be transformed into large amplitude narrow band low-frequency oscillation response, which can greatly improve the harvesting effectiveness of broadband vibration energy.