Provided is an audio encoding and decoding apparatus and method for improving a compression ratio while maintaining sound quality when sinusoidal waves of an audio signal are connected and encoded. The audio encoding method includes connecting sinusoidal waves of an input audio signal, converting a frequency of each of the connected sinusoidal waves to a psychoacoustic frequency, performing a first encoding operation for encoding the psychoacoustic frequency, performing a second encoding operation for encoding an amplitude of each of the connected sinusoidal waves, and outputting an encoded audio signal comprising the encoding result of the first encoding operation and the encoding result of the second encoding operation.