The automatic extraction of airport runway areas from high-resolution Synthetic Aperture Radar (SAR) images is of great research significance in the military and civilian fields. However, it is still challenging to distinguish the airport from surrounding objects in SAR images. In this paper, a new framework is proposed to extract airport runway areas (runways, taxiways, packing lots, and aircrafts) in a fast and automatic manner. The framework is based on the Geospatial Contextual Attention Mechanism (GCAM) for geospatial feature learning and classification, which is employed together with the downsampling and coordinate mapping modules. To evaluate the performance of the proposed framework, three large-scale Gaofen-3 SAR images with 1m resolution are utilized in the experiment. According to the results, Mean Pixels Accuracy (MPA) and Mean Intersection Over Union (MIOU) of the GCAM are 0.9850 and 0.9536, respectively, which outperform RefineNet, DeepLabV3+, and MDDA. The training time of GCAM for the dataset is 2.25h, and the average testing time for the five SAR images is only 18.15s. Therefore, GCAM can offer rapid and automatic airport detection from high-resolution SAR images with high accuracy, which can further be employed to mark the airport to greatly improve the detection accuracy of the aircrafts.