In this article, the compressed sensing reconstruction algorithm is incorporated into the Hadamard ghost imaging scheme to recover the information of objects to be measured at a lower sampling rate. The proposed scheme has fewer reconstruction times than the Hadamard ghost imaging scheme, and the required sampling time is also reduced. Observation time and structural similarity index are considered the objective evaluation norm for image reconstruction results of Hadamard ghost imaging scheme, which uses subspace pursuit (SP) algorithm and orthogonal matching pursuit (OMP) algorithm. After simulation and experimental verification, we conclude that the combination of the OMP algorithm and Hadamard ghost imaging scheme can result in faster imaging speed and better image quality.