Wind profile radar is an effective tool for detecting atmospheric wind field and turbulence. Its echo is liable to be interfered by ground clutter and becomes complicated. To improve detection precision of radar, ground clutter suppression is an important part of radar signal and spectrum processing. Current method of ground clutter suppression is introduced and its deficiency is analyzed, and the characteristics of ground clutter and radar atmospheric echo spectrum in frequency domain are investigated. Combined with gradient analysis of atmospheric echo spectrum, the method for suppressing ground clutter is described based on Gaussian least square quadratic fitting to the uncontaminated atmospheric echo spectrum. Results show that it is feasible to suppress ground clutter.