In the field of image processing using Synthetic Aperture Radar (SAR), aircraft detection is a challenging task. Conventional approaches always extract targets from the background of an image using image segmentation methods. Nevertheless, these methods mainly focus on pixel contrast and neglect the integrity of the target, which leads to locating the object inaccurately. In this study, we build a novel SAR aircraft detection framework. Compared to traditional methods, an improved saliency-based method is proposed to locate candidates coarsely and quickly in large scenes. This proposed method is verified to be more efficient compared with the sliding window method. Next, we design a convolutional neural network fitting in SAR images to accurately identify the candidates and obtain the final detection result. Moreover, to overcome the problem of limited available SAR data, we propose four data augmentation methods comprising translation, speckle noising, contrast enhancement, and small-angle rotation. Experimental results show that our framework achieves excellent performance on the high-resolution TerraSAR-X dataset.