The absorption of type-II nanostructures is often weaker than type-I counterpart due to spatially indirect optical transitions. This phenomenon limits the application of type-II nanostructures in photon detections. In this paper, we show that with proper arrangements of conduction barriers, the formation of quasi-bound states can significantly boost up the absorption of type-II coupled quantum rings. Meanwhile, the rapid tunneling of electrons in these leaky states should make the corresponding external quantum efficiency comparable to that of single (uncoupled) rings. These featuresmay improve the performance of photon detectors based on type-II semiconductor nanostructures.