This paper tackles the problem of table structure parsing (TSP) from images in the wild. In contrast to existing studies that mainly focus on parsing well-aligned tabular images with simple layouts from scanned PDF documents, we aim to establish a practical table structure parsing system for real-world scenarios where tabular input images are taken or scanned with severe deformation, bending or occlusions. For designing such a system, we propose an approach named Cycle-CenterNet on the top of CenterNet with a novel cycle-pairing module to simultaneously detect and group tabular cells into structured tables. In the cycle-pairing module, a new pairing loss function is proposed for the network training. Alongside with our Cycle-CenterNet, we also present a large-scale dataset, named Wired Table in the Wild (WTW), which includes well-annotated structure parsing of multiple style tables in several scenes like the photo, scanning files, web pages, emph{etc.}. In experiments, we demonstrate that our Cycle-CenterNet consistently achieves the best accuracy of table structure parsing on the new WTW dataset by 24.6% absolute improvement evaluated by the TEDS metric. A more comprehensive experimental analysis also validates the advantages of our proposed methods for the TSP task.