A liquid xenon calorimeter has recently been designed. The main purpose is to show the capability of observing monochromatic cosmic gamma ray lines in the 1∼100 GeV region. The calorimeter has a geometric factor of ∼1 m2·sr, an energy resolution of ∼0.4% and an angular resolution of about 1 degree for GeV-region gamma rays. These characteristics will meet the conditions required for the observation of gamma ray lines produced by the pair annihilation of hypothetical SUSY heavy Majorana fermions which might exist in the galactic halo as dark matter. The calorimeter is also applicable to the search for point sources emitting gamma rays as well as the investigation of diffuse gamma rays at high energies.