In this paper, we proposed a novel two-stage model that works in a hierarchical architecture to detect airports on synthetic aperture radar (SAR) images. In the first rough stage, an improved line segment detector (LSD) which tackles the line segments disconnection problem in SAR images is used to extract candidate airport regions coarsely. In the second fine stage, a well-trained Faster R-CNN with residual networks (ResNet) implementation (called ResFaster RCNN) is applied to each candidate regions to discriminate airport and non-airport regions and locate the airport much more precisely. Transfer learning and some improvement measures are applied to the networks. With this two-stage model, we can not only use both low-level and high-level features of airports synthetically but also avoid the information loss problem caused by resizing when large scene images are input into the networks. Experiments on large-scale SAR images have proved that the proposed method can reach a detection rate of 95% with low false alarm rate and show a great enhancement over other existing methods.