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Data hiding is the procedure of encoding desired information into a certain types of cover media (e.g. images) to resist potential noises for data recovery, while ensuring the embedded image has few perceptual perturbations. Recently, with the tremendous successes gained by deep neural networks in various fields, the research on data hiding with deep learning models has attracted an increasing amount of attentions. In deep data hiding models, to maximize the encoding capacity, each pixel of the cover image ought to be treated differently since they have different sensitivities w.r.t. visual quality. The neglecting to consider the sensitivity of each pixel inevitably affects the model's robustness for information hiding. In this paper, we propose a novel deep data hiding scheme with Inverse Gradient Attention (IGA), combining the idea of attention mechanism to endow different attention weights for different pixels. Equipped with the proposed modules, the model can spotlight pixels with more robustness for data hiding. Extensive experiments demonstrate that the proposed model outperforms the mainstream deep learning based data hiding methods on two prevalent datasets under multiple evaluation metrics. Besides, we further identify and discuss the connections between the proposed inverse gradient attention and high-frequency regions within images, which can serve as an informative reference to the deep data hiding research community. The codes are available at: https://github.com/hongleizhang/IGA.