It is a challenging work to design tamper recovery schemes for digital speech signal. Briefly, there are two problems need to be solved. One is that the signals used to tamper recovery are difficult to generate and embed, and the second is that it's hard to tamper location precisely for attacked speech signal. In this paper, compression and reconstruction method based on discrete wavelet transform (DWT) and discrete cosine transform (DCT) is given, to obtain the compressed signals used to tamper recovery. And then frame number and compressed signals are embedded based on block-based method. Attacked signal can be located by frame number, and compressed signals are extracted and used to reconstruct the attacked signal. Theory analysis and experimental results indicate that the scheme proposed not only improves the accuracy of tamper localization, but also can reconstruct the attacked signals.