This paper proposes a speech enhancement method for signals contaminated by room reverberation and additive background noise. The following conditions are assumed: (1) The spectral components of speech and noise are statistically independent Gaussian random variables. (2) The convolutive distortion channel is modeled as an auto-regressive system in each frequency bin. (3) The power spectral density of speech is modeled as an all-pole spectrum, while that of noise is assumed to be stationary and given in advance. Under these conditions, the proposed method estimates the parameters of the channel and those of the all-pole speech model based on the maximum likelihood estimation method. Experimental results showed that the proposed method successfully suppressed the reverberation and additive noise from three-second noisy reverberant signals when the reverberation time was 0.5 seconds and the reverberant signal to noise ratio was 10 dB.