  The f\'eeton is the gauge boson of the $U(1)_{B-L}$ gauge theory. If the
gauge coupling constant is extremely small, it becomes a candidate for dark
matter. We show that its decay to a pair of electron and positron explains the
observed Galactic 511-keV gamma-ray excess in a consistent manner. This
f\'eeton dark matter decays mainly into pairs of neutrino and anti-neutrino.
Future low-energy experiments with improved directional capability make it
possible to capture those neutrino signals. The seesaw-motivated parameter
space predicts a relatively short f\'eeton lifetime comparable to the current
cosmological constraint.
