As the performance of predictor is crucial to prediction-error based reversible data hiding, this study investigates a predictor using the least-square method to improve the prediction accuracy. The proposed predictor uses a checkerboard division to partition an image into two disjoint sets. One set is predicted by the other set using the prediction weights obtained by least-square method. The histogram-shifting method is then applied to the prediction errors to embed data. Because of better consideration for pixels' correlation, the proposed method gains more prediction improvement, and thus raises embedding capacity with less distortion. Experimental results show that the proposed method outperforms the existing prediction-error based reversible data hiding methods in terms of hiding capacity and visual quality.