In this paper, a new method of dual-threshold controlled adaptive clutter suppression is proposed for an airborne weather radar operated in the wind shear mode. To reliably estimate the center frequency and bandwidth of the clutter spectrum, the echo power in each range cell is used to design a dual-threshold controlled adaptive notch filter. This filter can reject the maximum amount of ground clutter, while reducing the effect of clutter residue on the wind shear signal. Results of our simulation have confirmed that this method has a superior clutter suppression performance, and can effectively improve the wind speed estimate accuracy of the wind shear signal.