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Most reversible data hiding (RDH) techniques have been evaluated by PSNR,which is based on MSE.Unfortunately,MSE turns out to be an extremely poor measure when the purpose is to predict perceived signal fidel-ity or quality.The structural similarity index has gained widespread popularity as an alternative motivating principle for the design of image quality measures.How to utilize the characterize of SSIM to design RDH algorithm is very critical.An optimal RDH algorithm under structural similarity constraint was proposed.Firstly,the metric of the structural similarity constraint was deduced.Secondly,the rate-distortion function of optimal structural similarity constraint was constructed,which was equivalent to minimize the average distortion for a given embedding rate.Fi-nally,the optimal transition probability matrix under the structural similarity constraint was obtained.Experiments show that the proposed method can be used to improve the performance of previous RDH schemes evaluated by SSIM.