Accurate segmentation of target boundary is the focus and difficulty of semantic segmentation of high-precision in-orbit satellite remote sensing images. Existing segmentation methods fail to accurately and effectively extract the boundary information, resulting in the boundary features being easily interfered by the image texture, which is not conducive to the accurate segmentation of remote sensing images. Therefore, we design a boundary-aware in-orbit satellite remote sensing image segmentation network (BASNet). Firstly, we propose the Boundary Extracting Module (BEM), BEM uses the information difference of the features in the adjacent layers of the network to explicitly model the boundary features and extracts the boundary features of all the targets of the remote sensing image. Secondly, the Boundary Feature Fusion Module (BFM) is designed to fully fuse the above boundary features into the features of each layer of the network, to enhance the network's representation of the target boundary features of the remote sensing images. And two different loss functions are designed to supervise the semantic segmentation network and the edge extraction network, respectively. Finally, experiments on two in-orbit remote sensing satellite datasets (Potsdam and Vaihingen) show that the method is more capable of representing boundary information compared to other similar methods. The network can alleviate the mis-classification problem of boundary pixels and improve the semantic segmentation performance of remote sensing images.