An audio signal interpolation apparatus is configured to perform interpolation processing on the basis of audio signals preceding and/or following a predetermined segment on a time axis so as to obtain an audio signal corresponding to the predetermined segment. The audio signal interpolation apparatus includes a waveform formation unit configured to form a waveform for the predetermined segment on the basis of time-domain samples of the preceding and/or the following audio signals and a power control unit configured to control power of the waveform for the predetermined segment formed by the waveform formation unit using a non-linear model selected on the basis of the preceding audio signal when the power of the preceding audio signal is larger than that of the following audio signal, or the following audio signal when the power of the preceding audio signal is smaller than that of the following audio signal.