Open-set recognition (OSR) from synthetic aperture radar (SAR) imageries plays a crucial role in maritime and terrestrial monitoring. Nevertheless, numerous deep learning-based SAR classifiers struggle with unknown targets outside of the training dataset, leading to a dilemma, namely that a large model is difficult to deploy, while a smaller one sacrifices accuracy. To address this challenge, the novel “LiOSR-SAR” lightweight recognizer is proposed for OSR in SAR imageries. It incorporates the compact attribute focusing and open-prediction modules, which collectively optimize its lightweight structure and high accuracy. To validate LiOSR-SAR, “fast image simulation using bidirectional shooting and bouncing ray (FIS-BSBR)” is exploited to construct the corresponding dataset. It enhances the details of targets for more accurate recognition significantly. Extensive experiments show that LiOSR-SAR achieves remarkable recognition accuracies of 97.9% and 94.1% while maintaining a compact model size of 7.5 MB, demonstrating its practicality and efficiency.