The correlation between images is crucial for solving the image co-segmentation problem that is segmenting common and salient objects from a set of related images. This paper proposes a novel co-attention computation block to compute the visual correlation between images for improving the co-segmentation performance. Here ‘co-attention’ means that we obtain the co-attention features in encoded features of an image to guide the attention in another image. To this purpose, we firstly introduce top-k average pooling to compute the channel co-attention descriptor. Then we explore the correlation between features in different spatial positions to get the spatial co-attention descriptor. Finally, these two types of co-attention descriptors are multiplied to generate a fused one. We obtain such a fused co-attention descriptor for each image and use it to produce the co-attention augmented feature map for the following processing in the applications. We embed the proposed co-attention block into a U-shaped Siamese network for fulfilling the image co-segmentation. It is proven to be able to improve the performance effectively in the experiments. To our best knowledge, it leads to the currently best results on Internet dataset and iCoseg dataset.