In order to solve the defect of the traditional spectral subtraction algorithm, an improved spectral subtraction based on the joint maximum a posteriori probability is proposed. The traditional spectral subtraction was used to reconstruct the speech via obtaining difference of the amplitude between the noisy speech and noise and extracting the phase of the noisy speech. "Music noise" was produced by the method, and the effect of signal enhancement under low signal-to-noise ratio was not ideal because of inaccurate phase estimation. For this, the multiband spectral subtraction and phase estimation were introduced, and spectral subtraction was carried out in the subbands which were obtained by spectrum division. And it has worked well on reducing the influence of "music noise". Meanwhile, the phase estimator based on the maximum a posteriori probability was constructed which was obtained by combining the amplitude function and thephase function of the signal and alternate iteration. The experimental results show that, compared with the traditional spectral subtraction, the proposed algorithm has performed better in terms of the quality perception and intelligibility of the enhanced speech at low signal to noise ratio.