In order to enhance the image quality of compressive sensing ghost Imaging (CSGI ) and solve the existing problems of measurement matrix in this stage,a new cons truction method of measurement matrix is presented in this paper.First,the princ iples and properties of deteiministic random sequences are introduced,which can be used as meas urement matrix and satisfy the restricted isometry property (RIP).Aiming at the nonnegativeness of light intensity,based on the deteiministic random sequences achieved by even quadratic cosine function ,a new construction method of measurement matrix is applied.Then,according to the theory of logistic map,the properties and accuracy of deteiministic random matrix are proved by simulation and the inf luences of initial value and the power of cosine function on the reconstruction property are analyzed.Finally,compared with Gaussian matrix,the experimental system platform is built,and the applicability and merit of deteiministic random matrix are analyzed.Experimental results indicate that the peak signal to noise ratio (PSNR) of the reconstructed image is 38.7dB and t he amount of data is reduced by 4096times compared with Gaussian matrix.It can satisfy the system requirements of stabilization,convenie nce and rapid speed in ghost imaging.