Compton camera is a promising instrument for nuclear material imaging in arms control scenarios. In planning to build a Compton camera to detect the symmetry of shielded nuclear materials, the energy spectrum of gamma-rays escaping from the Steve Fetter Nuclear Warhead model is obtained using Monte Carlo simulation. Then, a point model is defined for our study. The proposed Compton camera uses a 5-cm × 5-cm × 1-mm double-sided silicon strips detector as the scattering detector and a segmented ϕ5.08 × 5.08-cm NaI(Tl) array as the absorbing detector. How high-energy gamma-rays impact low-energy characteristic gamma-ray imaging is studied. The result shows that high-energy gamma-rays will reduce the imaging accuracy and signal-to-noise ratio. The holistic angle resolution measured can reach 4.15 deg by all characteristic gamma-rays. The symmetry research result shows that the Compton camera can detect the symmetry property of a nuclear warhead with obvious symmetry or asymmetry.