(1) Background: Gamma cameras have wide applications in industry, including nuclear power plant monitoring, emergency response, and homeland security. The desirable properties of a gamma camera include small weight, good resolution, large field of view (FOV), and wide imageable source energy range. Compton cameras can have a 4π FOV but have limited sensitivity at low energy. Coded-aperture gamma cameras are operatable at a wide photon energy range but typically have a limited FOV and increased weight due to the thick heavy metal collimators and shielding. In our lab, we previously proposed a 4π-view gamma imaging approach with a 3D position-sensitive detector, with which each detector element acts as the collimator for other detector elements. We presented promising imaging performance for 99mTc, 18F, and 137Cs sources. However, the imaging performance for middle- and high-energy sources requires further improvement. (2) Methods: In this study, we present a new gamma camera design to achieve satisfactory imaging performance in a wide gamma energy range. The proposed gamma camera consists of interspaced bar-shaped GAGG (Ce) crystals and tungsten absorbers. The metal bars enhance collimation for high-energy gamma photons without sacrificing the FOV. We assembled a gamma camera prototype and conducted experiments to evaluate the gamma camera’s performance for imaging 57Co, 137Cs, and 60Co point sources. (3) Results: Results show that the proposed gamma camera achieves a positioning accuracy of < 3° for all gamma energies. It can clearly resolve two 137Cs point sources with 10° separation, two 57Co and two 60Co point sources with 20° separation, as well as a 2 × 3 137Cs point-source array with 20° separation. (4) Conclusions: We conclude that the proposed gamma camera design has comprehensive merits, including portability, 4π-view FOV, and good angular resolution across a wide energy range. The presented approach has promising potential in nuclear security applications.