To provide an audio encoding device in which average processing amount is reduced by decreasing the number of times of a search for a quantization step size, thereby improving search precision.

As adaptive convergence processing A, a global gain for operating the quantization step size is found, a frequency spectrum is quantized based upon the found global gain, and the generated code amount of the quantized data obtained by the quantization is found. The generated code amount is compared with a target code amount and when a predetermined condition is not met, the adaptive convergence processing A is performed again, but a generated code amount variation amount when the global gain is varied by one is found, the global gain used for the last adaptive convergence processing A is corrected based thereupon, and the adaptive convergence processing A is carried out using the corrected global gain.