Due to the complexity and uncertainty of noise in acoustic environment, the traditional multichannel speech enhancement algorithm has insufficient noise suppression effect, resulting in a poor auditory experience. To solve this problem, an improved TFGSC and improved post filter speech enhancement algorithm was proposed in this paper. The algorithm used the maximum likelihood method to obtain the power spectral density of the target speech signal and noise signal, and then proposed an improved TFGSC which used the variable step normalized least mean square algorithm obtained by the signal power spectral density ratio. An improved optimally modified log spectral spectrum estimator was also proposed using the estimated speech presence probability by combining the signal power spectral density ratio and a priori signal to noise ratio. The simulation experiments in different SNR environments show that the algorithm proposed in this paper can effectively filter coherent noise and incoherent noise. Compared with other algorithms, the enhanced speech signal has higher SNR and speech quality.