For the Difference Expansion-Histogram Shifting (DE-HS) based reversible watermarking, improving the prediction accuracy helps to decrease the prediction errors, resulting in higher embedding capacity at the same embedding distortion. To predict image pixels more accurately, an LASSO (Least Absolute Shrinkage and Selection Operator) based local predictor was proposed. Specifically, by taking into account the fact that there exist edges and textures in natural images, the problem of image pixel prediction was formulated as the optimization problem of LASSO, then the prediction coefficients were obtained by solving the optimization problem, generating prediction errors accordingly. By applying the technique of DE-HS on the yielded prediction errors, an LASSO-based reversible watermarking scheme was designed. The experimental results show that compared with the least-square-based predictor, the proposed scheme has higher Peak Signal-to-Noise Ratio (PSNR) when embedding the same data.