An audio encoding method and apparatus, and an audio decoding method and apparatus, for processing a death sinusoid and a general continuation sinusoid. Using the unique characteristic of a death sinusoid, in that the death sinusoid has a tendency such that an amplitude component of the death sinusoid is less than that of a previous sinusoid, a method of adding an encoding syntax by distinguishing a general continuation sinusoid from a death sinusoid is provided. That is, when difference coding of the amplitude component of a death sinusoid is performed, the number of bits used when a negative number is coded is less than the number of bits used when a positive number is coded, in a Huffman table. By using this method, a bit rate in an entire coding decreases.