Aiming at the suppressing the noise under the circumstance of non - stationary and multiple noise is limited, the speech enhancement algorithm based on coherent filtering of the minimum tracking noise power spectrum estimation and generalized sidelobe canceller is proposed. The method uses the coherent filtering of the minimum tracking noise power spectrum to suppress the weak correlation noise, and then combines the generalized sidelobe canceller and the voice activity detection to suppress the strong correlation noise. The experimental results show that this method can effectively suppress the influence of noise and improve the intelligibility of speech.