Design and realization of random measurement scheme for compressed sensing (CS) are presented in this paper, and lower limits of the measurement number are achieved when the precise reconstruction is realized. Four kinds of random measurement matrices are designed according to the constraint conditions of random measurement. The performance is tested employing the algorithm of stagewise orthogonal matching pursuit (StOMP). Results of the experiment show that lower limits of the measurement number are much better than the results described in Refs.[13-15]. When the ratios of measurement to sparsity are 3.8 and 4.0, the mean relative errors of the reconstructed signals are 8.57 × 10^–13 and 2.43 × 10^–14, respectively, which confirms that the random measurement scheme of this paper is very effective.