A method and an apparatus for encoding a digital audio signal are provided. The method comprises the steps of: mapping the digital audio signal into a plurality of sub-bands and outputting the mapped sub-band signals; allocating a number of bits to each sub-band signal according to human psychoacoustic properties, on the basis of the mapped sub-band signals; compensating each sub-band signal by receiving a transmitted previous quantized error, quantizing the compensated sub-band signals according to the corresponding allocated bit number, and transferring the current quantized error to the next quantization; and forming a transmit bit stream in frame units from the quantized data. Therefore, the quantized error generated during encoding of the audio signal is can be minimized.