Traditional scintillator-based or semiconductor-based Compton cameras generally use the method of pixelation detector to obtain the interaction position of \(\gamma\) -rays with detectors, which suffers from the disadvantages of complex process, high cost, strong dependence on pixelation size for position resolution, and huge electronic readout system. These disadvantages limit the development of miniaturization and commercialization of Compton cameras. In this study, we used a whole GAGG crystal-coupled silicon photomultiplier (SiPM) array to build two types of detectors, namely side-readout-type detector and back-readout-type detector, and developed two kinds of position reconstruction algorithms, namely the response function method and the photon distribution reconstruction method. The position resolution of the two types of detectors was evaluated, and the position resolutions of the side-readout-type detector and back-readout-type detector were 1.2 mm and 1.6 mm, respectively. In addition, we built a prototype of a double-layer Compton camera based on a monolithic GAGG crystal using a side-readout-type detector as a scattering detector and a back-readout-type detector as an absorption detector. The position resolution of the radioactive source was 5.4 mm, with the source placed 27 mm away from the scattering detector.