Abstract: Aiming at the difficulty of modeling the gauss measurement of speech signal for its strong randomicity under compressed sensing theory, this paper proposed Volterra model of compressed sensing measurement of speech signal based on special row echelon measurement matrix, and realized the prediction of compressed sensing measurement of speech signal based on this kind of Volterra model .The prediction effects of input dimensions and order of Volterra model were studied. Wiener filter was used in order to ruduce the prediction error of Volterra model. Under the same known data quantity, reconstruction based on part of compressed sensing measurement, Volterra model and wiener filter, achieves better reconstruction performance than that of gauss measurement. Research on this model offered certain reference value on the combination of compressed sensing and speech signal processing techniques.