In　this　paper,　we　propose　a　lightweight　privacy-preserving　Faster　R-CNN　framework　(SecRCNN)　for　object　detection　in　medical　images.　Faster　R-CNN　is　one　of　the　most　outstanding　deep　learning　models　for　object　detection.　Using　SecRCNN,　healthcare　centers　can　efficiently　complete　privacy-preserving　computations　of　Faster　R-CNN　via　the　additive　secret　sharing　technique　and　edge　computing.　To　implement　SecRCNN,　we　design　a　series　of　interactive　protocols　to　perform　the　three　stages　of　Faster　R-CNN,　namely　feature　map　extraction,　region　proposal　and　regression　and　classification.　To　improve　the　efficiency　of　SecRCNN,　we　improve　the　existing　secure　computation　sub-protocols　involved　in　SecRCNN,　including　division,　exponentiation　and　logarithm.　The　newly　proposed　sub-protocols　can　dramatically　reduce　the　number　of　messages　exchanged　during　the　iterative　approximation　process　based　on　the　coordinate　rotation　digital　computer　algorithm.　Moreover,　the　effectiveness,　efficiency　and　security　of　SecRCNN　are　demonstrated　through　comprehensive　theoretical　analysis　and　extensive　experiments.　The　experimental　findings　show　that　the　communication　overhead　in　computing　division,　logarithm　and　exponentiation　decreases　to　36.19%,　73.82%　and　43.37%,　respectively.