Instance segmentation in high-resolution (HR) remote sensing imagery is one of the most challenging tasks and is more difficult than object detection and semantic segmentation tasks. It aims to predict class labels and pixel-wise instance masks to locate instances in an image. However, there are rare methods currently suitable for instance segmentation in the HR remote sensing images. Meanwhile, it is more difficult to implement instance segmentation due to the complex background of remote sensing images. In this article, a novel instance segmentation approach of HR remote sensing imagery based on Cascade Mask R-CNN is proposed, which is called a high-quality instance segmentation network (HQ-ISNet). In this scheme, the HQ-ISNet exploits a HR feature pyramid network (HRFPN) to fully utilize multi-level feature maps and maintain HR feature maps for remote sensing images' instance segmentation. Next, to refine mask information flow between mask branches, the instance segmentation network version 2 (ISNetV2) is proposed to promote further improvements in mask prediction accuracy. Then, we construct a new, more challenging dataset based on the synthetic aperture radar (SAR) ship detection dataset (SSDD) and the Northwestern Polytechnical University very-high-resolution 10-class geospatial object detection dataset (NWPU VHR-10) for remote sensing images instance segmentation which can be used as a benchmark for evaluating instance segmentation algorithms in the high-resolution remote sensing images. Finally, extensive experimental analyses and comparisons on the SSDD and the NWPU VHR-10 dataset show that (1) the HRFPN makes the predicted instance masks more accurate, which can effectively enhance the instance segmentation performance of the high-resolution remote sensing imagery; (2) the ISNetV2 is effective and promotes further improvements in mask prediction accuracy; (3) our proposed framework HQ-ISNet is effective and more accurate for instance segmentation in the remote sensing imagery than the existing algorithms.