In the compressed sensing theory, to accurately reconstruct signal, the measurement matrix must restrict condition of restricted isometry property (RIP), most of the random matrix satisfy this condition, and can be used as the measurement matrix, such as Gauss, Fourier and Bernoulli random matrix. Among them, Gauss random matrix is an common measurement matrix. However, the effect of this kind of matrix reconstructed signal is not very satisfactory. In this paper, we mainly deal with the above problems of Gauss random matrix. The improved measurement matrix preserves the random independence of Gauss random matrix, and satisfies the condition of RIP. the performance of the improved measurement matrix is verified by the reconstruction of compressed sensing in time domain, and then it is extended to the transform domain compressed sensing reconstruction. The experimental results show that the improved measurement matrix has better performance than the original Gauss random matrix.