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Currently, single image inpainting has achieved promising results based on deep convolutional neural networks. However, inpainting on stereo images with missing regions has not been explored thoroughly, which is also a significant but different problem. One crucial requirement for stereo image inpainting is stereo consistency. To achieve it, we propose an Iterative Geometry-Aware Cross Guidance Network (IGGNet). The IGGNet contains two key ingredients, i.e., a Geometry-Aware Attention (GAA) module and an Iterative Cross Guidance (ICG) strategy. The GAA module relies on the epipolar geometry cues and learns the geometry-aware guidance from one view to another, which is beneficial to make the corresponding regions in two views consistent. However, learning guidance from co-existing missing regions is challenging. To address this issue, the ICG strategy is proposed, which can alternately narrow down the missing regions of the two views in an iterative manner. Experimental results demonstrate that our proposed network outperforms the latest stereo image inpainting model and state-of-the-art single image inpainting models.