This paper proposes a method based on modulation transfer function (MTF) to restore the power envelope of noisy reverberant speech by using a Kalman filter with linear prediction (LP). Its advantage is that it can simultaneously suppress the effects of noise and reverberation by restoring the smeared MTF without measuring room impulse responses. This scheme has two processes: power envelope subtraction and power envelope inverse filtering. In the subtraction process, the statistical properties of observation noise and driving noise for power envelope are investigated for the criteria of the Kalman filter which requires noise to be white and Gaussian. Furthermore, LP coefficients drastically affect the Kalman filter performance, and a method is developed for deriving LP coefficients from noisy reverberant speech. In the dereverberation process, an inverse filtering method is applied to remove the effects of reverberation. Objective experiments were conducted under various noisy reverberant conditions to evaluate how well the proposed Kalman filtering method based on MTF improves the signal-to-error ratio (SER) and correlation between restored power envelopes compared with conventional methods. Results showed that the proposed Kalman filtering method based on MTF can improve SER and correlation more than conventional methods.