Audio data hiding techniques have been applied various applications such as audio watermarking and steganography. In this paper, we propose an audio data hiding method based on the phase information of the modulated complex lapped transform (MCLT) coefficients and evaluate the performance in terms of audio quality and robustness. To embed and extract the data, the proposed technique modifies the phases of the MCLT coefficients of the audio signal to be a desired value at the receiver. The proposed method is available to transmit data at relatively high data rate with low quality degradation. Moreover, the experimental results show that the proposed method is considered robust against various attacks consisting of signal processing, overwriting using data hiding methods, and malicious removal attacks except time scaling attack.