In this paper, we present a novel data hiding scheme based on the minimum distortion look-up table (LUT) embedding that achieves good distortion-robustness performance. We first analyze the distortion introduced by LUT embedding and formulate its relationship with run constraints of LUT. Subsequently, a Viterbi algorithm is presented to find the minimum distortion LUT. Theoretical analysis and numerical results show that the new LUT design achieves not only less distortion but also more robustness than the traditional LUT based data embedding schemes.