The reversible data hiding allows original image to be completely recovered from the stego image when the secret data has been extracted, it is has drawn a lot of attentions from researchers. In this paper, a novel Taylor Expansion (TE) based stereo image reversible data hiding method is presented. Since the prediction accuracy is essential to the data hiding performance, a novel TE based predictor using correlations of two views of the stereo image is proposed. TE can fully exploit strong relationships between matched pixels in the stereo image so that the accuracy of the prediction can be improved. Then, histogram shifting is utilized to embed data to decrease distortion of stereo images, and multi-level hiding can increase embedding capacity. Experimental results show that the proposed method is superior to some existing data hiding methods considering embedding capacity and the quality of the stego stereo images.