The 2D virtual try-on task aims to transfer a target clothing image to the corresponding region of a person image. Although an extensive amount of research has been conducted due to its immense applications, this task still remains a great challenge to handle some complicated issues (e.g., non-rigid shapes, large occlusions and arbitrary poses). To this end, we propose a novel network with structural and textural consistency-preserving mechanism for producing high-fidelity try-on images. Specifically, we first generate the semantic layout of a clothing-agnostic person to obtain the segmentation map, which is used as the transforming conditions of the target clothes. Based on a recurrent network structure, the transform lookup is performed to iteratively update a dense flow. Then, we adopt a thin-plate-spline-based warping method to estimate the coarse offset flow for all key-point positions. Guided by this sparse flow, a multi-scale deformable convolution module is designed to further iteratively predict the fine offsets for densely sampled positions, by which the clothing item and person shape can be accurately aligned. Finally, we develop a refinement module to effectively fuse the global and local features, which can render accurate geometric structures of the body parts and maintain texture sharpness of the clothes. Extensive experiments on benchmark datasets demonstrate that our method outperforms other state-of-the-art methods in terms of quantitative and qualitative try-on results. The code is available on: https://github.com/TJU-WEIHAO/MLCN .