An audio encoding method comprising: an orthogonal transformation step of transforming an input audio signal into frequency components for each frame; a gain calculation step of separating the frequency components obtained at the orthogonal transforming step in units of spectrum band such that each band consists of a plurality of frequency components, calculating, for each band, a gain, referred to as an initial gain , for scaling each of the frequency components of said band, based on a permissible quantization noise for said band and its frequency components , and correcting each initial gain by using a past gain used in the same band as said each initial gain in a past frame, thereby calculating a corrected gain ; a quantization step of generating a quantized signal by scaling and quantizing, for each band, its frequency components by using the corrected gain obtained in the gain calculation step; a gain encoding step of generating and encoding gain information for each band; and a multiplexing step of generating encoded audio data by multiplexing, for each band, the quantized signal obtained in the quantization step and the gain information obtained in the gain encoding step, wherein the gain encoding step comprises using a gain selected from past gains of a predetermined number of previous frames as the past gain, calculating a difference gain for each band by subtracting the past gain and an average value from the corrected gain obtained in the gain calculation step, the average value being an average value of differences between the corrected gains and the past gains with respect to the plurality of bands, and generating the gain information by encoding the difference gain, the average value, and frame number information of the selected frame. an orthogonal transformation step of transforming an input audio signal into frequency components for each frame; a gain calculation step of separating the frequency components obtained at the orthogonal transforming step in units of spectrum band such that each band consists of a plurality of frequency components, calculating, for each band, a gain, referred to as an initial gain , for scaling each of the frequency components of said band, based on a permissible quantization noise for said band and its frequency components , and correcting each initial gain by using a past gain used in the same band as said each initial gain in a past frame, thereby calculating a corrected gain ; a quantization step of generating a quantized signal by scaling and quantizing, for each band, its frequency components by using the corrected gain obtained in the gain calculation step; a gain encoding step of generating and encoding gain information for each band; and a multiplexing step of generating encoded audio data by multiplexing, for each band, the quantized signal obtained in the quantization step and the gain information obtained in the gain encoding step, wherein the gain encoding step comprises using a gain selected from past gains of a predetermined number of previous frames as the past gain, calculating a difference gain for each band by subtracting the past gain and an average value from the corrected gain obtained in the gain calculation step, the average value being an average value of differences between the corrected gains and the past gains with respect to the plurality of bands, and generating the gain information by encoding the difference gain, the average value, and frame number information of the selected frame. <EOS>