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In this paper, we propose a high efficiency deterministic measurement matrix for practical compressive sensing based on the combination of Logistic Chaotic system and correlation, called Chaos-Gaussian measurement matrix. Initially, deterministic Logistic system has been used to generate Chaotic sequence with good pseudo-random. Subsequently, two spread spectrum sequences have been constructed and been verified to follow Gaussian distribution. On the basis of the observation mentioned previously, Chaos-Gaussian measurement matrix is constructed. Experimental results corroborate that Chaos-Gaussian measurement matrix is superior to Gaussian and Bernoulli random measurement matrix. Furthermore, Chaos-Gaussian measurement matrix balances the randomness and the certainty.