The presence of radio-frequency interference (RFI) contaminates data collected by synthetic aperture interferometric radiometers (SAIRs). The performances of current RFI detection methods are limited due to insufficient exploration of RFI characteristics. This paper proposes a new RFI source detection method based on a convolutional neural network (CNN) that exploits side-lobe characteristics of the array factor of SAIR systems. Based on the common characteristic observed in RFI images, namely the presence of hexagonal tailings extended from a local peak of the RFI source, this method incorporates the hexagonal tailing feature into the detection scope, thereby expanding the capability to identify RFI. By including the hexagonal tailing feature, the method enhances the comprehensiveness and accuracy of RFI detection. This inclusion leads to a more comprehensive and accurate detection range for RFI sources. Results using real SMOS satellite data demonstrate that the proposed method has improved detection performance compared with traditional approaches that are commonly used in RFI detection tasks for SAIRs.