Watermarking is the procedure of encoding desired information into an image to resist potential noises while ensuring the embedded image has little perceptual perturbations from the original image. Recently, with the tremendous successes gained by deep neural networks in various fields, digital watermarking has attracted increasing number of attentions. The neglect of considering the pixel importance within the cover image of deep neural models will inevitably affect the model robustness for information hiding. Targeting at the problem, in this paper, we propose a novel deep watermarking scheme with Inverse Gradient Attention (IGA), combing the ideas of adversarial learning and attention mechanism to endow different importance to different pixels. With the proposed method, the model is able to spotlight pixels with more robustness for embedding data. Besides, from an orthogonal point of view, in order to increase the model embedding capacity, we propose a complementary message coding module. Empirically, extensive experiments show that the proposed model outperforms the state-of-the-art methods on two prevalent datasets under multiple settings.