The wind-induced vibration energy harvesting technology plays an important role in the vibration energy harvesting technology, which has the potential to supply electrical energy for the wireless sensors. This paper studies the output response of nonlinear tristable wind-induced vibration energy harvester, establishes the dynamic model of the harvester, and the output response are compared for the harvester with symmetric and asymmetric potential wells. The results indicate that the tristable wind-induced vibration energy harvester with asymmetric potential wells has lower initial working wind speed and wider wind speed region for the large-amplitude oscillation compared with the harvester with symmetric potential wells. In addition, the output responses of the harvester with different external resistance, equivalent mass and stiffness are compared, and the results suggest that at the fixed wind speed, the output voltage increases with the increasing of the external resistance. When the external resistance is larger than 10 MΩ, the changes of the output voltage slow down. Finally, the numerical results indicate that the equivalent mass and the linear stiffness term influence the initial working wind speed and the effective working region of the harvester.