To solve the problem that contrast enhancement effect is affected by the embedding rate in most existing Reversible Data Hiding (RDH) algorithms, a new RDH method based on texture partition for medical images was proposed. Firstly, the contrast of an image was stretched to enhance image contrast, and then according to the characteristics of medical image texture, the medical image was divided into high and low texture levels. The key partion of the medical image mainly had high texture level. To enhance the contrast of high texture level further and guarantee the infomation embedding capacity, different embedding processes were adopted for high and low texture levels. In order to compare the effect of contrast enhancement between the proposed method and other RDH algorithms for medical images, No-Reference Contrast-Distorted Images Quality Assessment (NR-CDIQA) was adopted as the evaluation standards. The experimental results show that the marked images processed by the proposed method can get better NR-CDIQA and contrst enhancement in different embedding rate.