Digital image watermarking seeks to protect the digital media information from unauthorized access, where the message is embedded into the digital image and extracted from it, even some noises or distortions are applied under various data processing including lossy image compression and interactive content editing. Traditional image watermarking solutions easily suffer from robustness when specified with some prior constraints, while recent deep learning-based watermarking methods could not tackle the information loss problem well under various separate pipelines of feature encoder and decoder. In this paper, we propose a novel digital image watermarking solution with a compact neural network, named Invertible Watermarking Network (IWN). Our IWN architecture is based on a single Invertible Neural Network (INN), this bijective propagation framework enables us to effectively solve the challenge of message embedding and extraction simultaneously, by taking them as a pair of inverse problems for each other and learning a stable invertible mapping. In order to enhance the robustness of our watermarking solution, we specifically introduce a simple but effective bit message normalization module to condense the bit message to be embedded, and a noise layer is designed to simulate various practical attacks under our IWN framework. Extensive experiments demonstrate the superiority of our solution under various distortions.