The invention is related to a wind power generator with controllable power output, which comprises an elastic tail rod and a tail wing. One end of the elastic tail rod connects with the wind power generator; the other end of the elastic tail rod connects with the tail wing. The yaw center for the wind power generator deviates from its center line. With this shifted yaw center and the elastic tail rod, the tail wing and the elastic tail rod do not deform, or deform only a little to keep the power generator in the wind direction to acquire the maximum wind energy before reaching the rated power wind speed. Furthermore, when the wind speed exceeds the rated power wind speed, the tail wing and the elastic tail rod will bend more to force the wind power generator at a certain angle with the wind direction to control the wind power generator in a constant rated power output and to protect the wind power generator as well as the turbine blades.