An encoding apparatus and a decoding apparatus for reducing the quantization error of a G.711 codec and improving sound quality are provided. The encoding apparatus includes a G.711 encoder which generates a G.711 bitstream by encoding an input audio signal; an enhancement-layer encoder which chooses one of a static bit allocation method and a dynamic bit allocation method that can produce less quantization error based on the input audio signal and the G.711 bitstream, and outputs an enhancement-layer bitstream including encoded additional mantissa information obtained by using the chosen bit allocation method; and a multiplexer which multiplexes the G.711 bitstream and the enhancement-layer bitstream. Therefore, it is possible to reduce the quantization error of a G.711 codec and improve sound quality.