In view of the poor performance of generalized sidelobe canceller （GSC） of incoherent noise cancellation， an improved GSC denoising algorithm with post-Kalman filter is proposed. The algorithm corrects the adaptive noise canceller through the normalized least mean square algorithm， outputs the speech signal after filtering the directional interference noise to the Kalman filter， and iterates the residual background noise with the minimum mean square error （MMSE） to suppress incoherent noise and thermal noise generated by microphone array elements. After the objective speech quality evaluation， perceptual evaluation of speech quality （PESQ）， and spectrogram analysis under different signal-to-noise ratio conditions， it is proved that compared with the traditional GSC and the improved GSC of post-spectral subtraction， this algorithm is better at noise elimination. The performance is better， and the enhanced signal is closer to the target signal.