This paper proposes a novel signal processing method to extract the wind velocity at one altitude in the k-band wind radar based on the Gauss cost function (GCF). Traditional methods only consider the spatial continuity of turbulence, leading to significant fluctuations in the calculated wind velocity when strong clutter interference is present in the spectrum. Therefore, we consider the temporal continuity of turbulence, when the frequency offset of the clutter significantly deviates from the previous frequency, the Gauss function is used to reshape the current spectrum and amplify the turbulence signal interfered with clutter. Then, using the cost function to estimate the wind velocity at each moment and calculate the parameters required for the Gauss function. The GCF algorithm can effectively improve the signal-to-noise ratio (SNR) by 2 dB and increase radar detection accuracy by 10%.