The sound transmission of a spherical wave through a double plate structure is theoretically and numerically analyzed. Unlike the plane wave incidence, it is demonstrated that the sound transmission loss due to the spherical sound wave incidence follows a law of 9 dB/oct for a double-layered infinite plate. For a double-layered finite plate, the sound transmission loss is lying in between 9 dB/oct and 18 dB/oct in most frequency ranges, and depends heavily on the size and position of the plate relative to the source.