We study the effect of normalization on single domain generalization, the goal of which is to learn a model that performs well on many unseen domains with only single do-main data for training. We propose a new type of normalization, LSLR , that has an adaptive form that generalizes other normalizations. The key idea is to learn both the standardization and rescaling statistics for normalization with neural networks. This new normalization has better adaptivity and is capable of helping model generalize better for single domain generalization with a robust objective. Combined with adversarial domain augmentation methods, we can optimize the robust objective approximately. We show that our method consistently outperforms the baselines and achieves state-of-the-art results on three standard bench-marks for single domain generalization.