Image-based virtual try-on systems for fitting a new in-shop clothes into a person image have attracted increasing research attention, yet is still challenging. A desirable pipeline should not only transform the target clothes into the most fit shape seamlessly but also preserve well the clothes identity in the generated image, that is, the key characteristics (e.g. texture, logo, embroidery) that depict the original clothes. However, previous image-conditioned generation works fail to meet these critical requirements towards the plausible virtual try-on performance since they fail to handle large spatial misalignment between the input image and target clothes. Prior work explicitly tackled spatial deformation using shape context matching, but failed to preserve clothing details due to its coarse-to-fine strategy. In this work, we propose a new fully-learnable Characteristic-Preserving Virtual Try-On Network (CP-VTON) for addressing all real-world challenges in this task. First, CP-VTON learns a thin-plate spline transformation for transforming the in-shop clothes into fitting the body shape of the target person via a new Geometric Matching Module (GMM) rather than computing correspondences of interest points as prior works did. Second, to alleviate boundary artifacts of warped clothes and make the results more realistic, we employ a Try-On Module that learns a composition mask to integrate the warped clothes and the rendered image to ensure smoothness. Extensive experiments on a fashion dataset demonstrate our CP-VTON achieves the state-of-the-art virtual try-on performance both qualitatively and quantitatively.