Abstract: Currently, two types of problems exist in the design of measurement matrices in compressed sensing. One is that random measurement matrices are difficult to be realized by hardware. The other is that the size of deterministic matrices which are based on polynomials or algebraic curves cannot be arbitrary. To cope with these problems, this paper introduced a measurement matrices construction method based on deterministic random sequences. The proof that the matrices satisfy the Restricted Isometry Property (RIP) was also given in the paper. In the simulation experiments, the proposed matrices were compared with Gaussian random matrices, Bernoulli matrices, sparse matrices and chaotic matrices. Experiment results show that the matrices designed by the proposed strategy have equal performance with other popular measurement matrices. Also，deterministic random matrices are used for speech compression and reconstruction. Subjective and objective evaluation results of speech quality both show that the proposed matrices exhibit excellent performance in speech reconstruction.