Recent studies have proven that DNNs, unlike human vision, tend to exploit texture information rather than shape. Such texture bias is one of the factors for the poor generalization performance of DNNs. We observe that the texture bias negatively affects not only in-domain generalization but also out-of-distribution generalization, i.e., Domain Generalization. Motivated by the observation, we propose a new framework to reduce the texture bias of a model by a novel optimization-based data augmentation, dubbed Stylized Dream. Our framework utilizes adaptive instance normalization (AdaIN) to augment the style of an original image yet preserve the content. We then adopt a regularization loss to predict consistent outputs between Stylized Dream and original images, which encourages the model to learn shape-based representations. Extensive experiments show that the proposed method achieves state-of-the-art performance in out-of-distribution settings on public benchmark datasets: PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet.