An apparatus for processing an audio signal and method thereof are disclosed, by which a local dynamic range of an audio signal can be adaptively normalized as well as a maximum dynamic range of the audio signal. The present invention includes receiving a signal, by an audio processing apparatus; computing a long-term power and a short-term power by estimating power of the signal; generating a slow gain based on the long-term power; generating a fast gain based on the short-term power; obtaining a final gain by combining the slow gain and the fast gain; and, modifying the signal using the final gain.