In this paper, a new method of dual-threshold controlled adaptive clutter suppression is proposed for airborne weather radar which is operated in wind shear mode. On the basis of validly estimating the center frequency and bandwidth of clutter spectrum, the echo power in each range cell is used to design a dual-threshold controlled adaptive notch filter. This filter can provide a maximum extent possibility to reject the ground clutter, and meanwhile reduce the effect of clutter residue on wind shear signal. Results of simulation have proved that this method has a superior clutter suppression performance, and can effectively improve the wind speed estimate accuracy of the wind shear signal.