In this paper, a new stereo image watermarking scheme using the discrete wavelet transform (DWT) and adaptive disparity estimation is proposed. First, a watermark data is embedded into the right image of a stereo image pair by using the conventional DWT operation. Here, the right image is decomposed into three-level by DWT and then the watermark is embedded into DWT coefficients using the characteristics of the human visual system. Second, the disparity data is extracted by using the watermarked right image and the left image. And then, both of this extracted disparity data and the left image are transmitted to the recipient through the communication channel. At the receiver, the watermarked right image is reconstructed from the received left image and disparity data by use of the adaptive matching algorithm. Basing on the difference between the discrete wavelet-transformed watermarked image and original right image, the embedded watermark image can be extracted from this reconstructed right image. From some experiments using the stereo images of the CCETT's 'Manege' and a watermark image of English alphabet 'NRL', it is found that the PSNRs of the reconstructed right images by using the proposed algorithm improve to 7.6dB for 'Manege' on average by comparing with those of the reconstructed right images through the conventional pixel-based matching algorithm, block-based matching algorithm and DWT-based algorithms. At the same time the PSNRs of the watermark image extracted from these reconstructed right images also improve to 6.51dB on average for 'Manege' images, respectively. These experimental results also suggest a possibility of practical implementation of the stereo image watermarking system based-on the adaptive matching algorithm and the discrete wavelet transform.