This paper addresses the problem of image matting for transparent objects. Existing approaches often require tedious capturing procedures and long processing time, which limit their practical use. In this paper, we formulate transparent object matting as a refractive flow estimation problem, and propose a deep learning framework, called TOM-Net, for learning the refractive flow. Our framework comprises two parts, namely a multi-scale encoder-decoder network for producing a coarse prediction, and a residual network for refinement. At test time, TOM-Net takes a single image as input, and outputs a matte (consisting of an object mask, an attenuation mask and a refractive flow field) in a fast feed-forward pass. As no off-the-shelf dataset is available for transparent object matting, we create a large-scale synthetic dataset consisting of $178K$ images of transparent objects rendered in front of images sampled from the Microsoft COCO dataset. We also capture a real dataset consisting of $876$ samples using $14$ transparent objects and $60$ background images. Besides, we show that our method can be easily extended to handle the cases where a trimap or a background image is available.Promising experimental results have been achieved on both synthetic and real data, which clearly demonstrate the effectiveness of our approach.