  The $O$(MeV) spin-1 U-boson has been proposed to mediate the interaction
among electron-positron and $O$(MeV) dark matter, in order to account for the
511 keV $\gamma$-ray observation by SPI/INTEGRAL. In this paper the
observability of such kind of U-boson at BESIII is investigated through the
processes $e^+e^- \to U \gamma$ and $e^+e^- \to J/\Psi \to e^+e^- U$. We find
that BESIII and high luminosity B-factories have the comparable capacity to
detect such U-boson. If U-boson decays mainly into dark matter, i.e. invisibly,
BESIII can measure the coupling among U-boson and electron-positron $g_{eR}$
(see text) down to $O(10^{-5})$, and cover large parameter space which can
account for 511 keV $\gamma$-ray observation. On the other hand, provided that
U decays mainly into electron-positron, BESIII can detect $g_{eR}$ down to
$O(10^{-3})$, and it is hard to explore 511 keV
  $\gamma$-ray measurement allowed parameter space due to the irreducible QED
backgrounds.
