A Minimum Mean Square Error (MMSE) speech enhancement algorithm based on Laplacian distribution was proposed to solve the problem of noise residual and speech distortion of speech enhanced by the spectral subtraction algorithm based on Gaussian distribution. Firstly, the original noisy speech signal was framed and windowed, and the Fourier transform was performed on the signal of each processed frame to obtain the Discrete-time Fourier Transform (DFT) coefficient of short-term speech. Secondly, the noisy frame detection was performed to update the noise estimation by calculating the logarithmic spectrum energy and spectral flatness of each frame. Thirdly, based on the assumption of Laplace distribution of speech DFT coefficient, the optimal spectral subtraction coefficient was derived under the MMSE criterion, and the spectral subtraction with the obtained coefficient was performed to obtain the enhanced signal spectrum. Finally, the enhanced signal spectrum was subjected to inverse Fourier transform and framing to obtain the enhanced speech. The experimental results show that the Signal-to-Noise Ratio (SNR) of the speech enhanced by the proposed algorithm is increased by 4.3 dB on average, and has 2 dB improvement compared with that of the speech enhanced by the over-subtraction method. In the term of Perceptual Evaluation of Speech Quality (PESQ) score, compared with that of over-subtraction method, the average score of the proposed algorithm has a 10% improvement. The proposed algorithm has better noise suppression and less speech distortion, and has a significant improvement in SNR and PESQ evaluation standards.