Detecting concealed objects, such as in vivo lesions or camouflage, requires customized imaging systems. Lensless cameras, being compact and flexible, offer a promising alternative to bulky lens systems. However, the absence of lenses leads to measurements lacking visual semantics, posing significant challenges for concealed object detection (COD). To tackle this issue, we propose a region gaze-amplification network (RGANet) for progressively exploiting concealed objects from lensless imaging measurements. Specifically, a region gaze module (RGM) is proposed to mine spatial-frequency cues informed by biological and psychological mechanisms, and a region amplifier (RA) is designed to amplify the details of object regions to enhance COD performance. Furthermore, we contribute the first relevant dataset as a benchmark to prosper the lensless imaging community. Extensive experiments demonstrate the exciting performance of our method. Our codes will be released in \url{https://github.com/YXJ-NTU/Lensless-COD}.