In this paper, a novel speech enhancement algorithm based on the MAP estimation is proposed. The proposed speech enhancer adaptively changes the speech spectral density used in the MAP estimation according to the sum of the observed power spectra. In a speech segment, the speech spectral density approaches to Rayleigh distribution to keep the quality of the enhanced speech. While in a non-speech segment, it approaches to an exponential distribution to reduce noise effectively. Furthermore, when the noise is super-Gaussian, we modify the width of Gaussian so that the Gaussian model with the modified width approximates the distribution of the super-Gaussian noise. This technique is effective in suppressing residual noise well. From computer experiments, we confirm the effectiveness of the proposed method.