The speech signal is different from the typical audio in terms of spectral bandwidth, intensity distribution, and signal continuity, thus how to achieve high imperceptibility and strong robustness for speech steganography is a big challenge. In this paper, we present a speech steganography scheme based on the parity-segmented method and the differential singular value decomposition (SVD). The selected discrete cosine transform (DCT) coefficients are divided into two segments according to parity order. In this way, the energy of the paired segments is approximately equal, therefore the changes in the singular values caused by data embedding are reduced, and high imperceptibility is achieved. Unlike the common SVD-based steganography, the differential SVD scheme can effectively remove the impact of amplitude scaling attack by embedding the secret message into the difference between the singular values. Experimental results show that the proposed method achieves high imperceptibility and strong robustness while resisting the state-of-the-art steganalytic methods. INDEX TERMS Steganography, differential SVD, paired segments, imperceptibility, amplitude scaling.