Aircraft detection in synthetic aperture radar (SAR) images is one challenging task due to the discreteness of aircraft scattering, the diversity of aircraft size, and the interference of background. In order to deal with these problems, a novel method named scattering enhancement and feature fusion network (SEFFNet) is here proposed to detect aircraft via combining traditional image processing and deep learning together. At first, a scattering information extraction and enhancement module (SIEEM) is proposed to highlight the scattering points of aircraft targets. Then, to more effectively focus on the location of aircraft targets, a space-to-depth coordinate attention module (SDCAM) is further designed, following which an efficient multi-scale feature fusion pyramid (FFP) is also introduced to fuse the semantic information of different layers. At last, a contextual fusion head (CFH) is built to improve the receptive field for better detecting aircraft. The experiments carried out on the popular datasets SADD and SAR-AIRcraft-1.0 show that SEFFNet is more appropriate for aircraft detection, especially the small-size aircraft detection, in comparison with other state-of-the-art (SOTA) methods. Taking the dataset SADD for example, on average, the precision, recall, F1-score, and APs values are respectively 2.8%, 2.6%, 2.7%, and 2.0% higher than the baseline network YOLOv5.