To overcome the influence of statistical noise on the reconstruction quality of computational ghost imaging under the random speckle patterns illumination, a new computational ghost imaging method based on orthogonal optimization of random speckle patterns is proposed. Firstly, the effect of random speckle patterns on the reconstruction quality of the target object is analyzed based on computational ghost imaging. Then, combining the properties of a real symmetric matrix, the original random speckle patterns are orthogonalized by a spatial mapping matrix. Further, the reconstructed orthogonal speckle patterns are used to irradiate the unknown object and the transmitted light is measured by a bucket detector. A series of measured values by bucket detectorand the reconstructed speckle patterns stored in the computer are used to reconstruct the target object through second-order correlation operation. Finally, according to the covariance matrix characteristics of the reconstructed speckle patterns, the reconstruction results are compensated to further improve the reconstruction quality of the object. This method can not only effectively improve the image quality of computational ghost imaging under the action of random speckle patterns, but also has the characteristics of simple algorithm structure. The simulation results show that the method can reconstruct the target effectively and has a good performance compared with the traditional computational ghost imaging under the illumination of random speckle patterns.