  We investigate the rare electromagnetic decays of neutral vector mesons
(exemplified by $J/\psi$, $\Upsilon$, $\rho^0$, $\omega,\phi$, \ldots) into
four charged leptons ($2(e^+e^-)$, $2(\mu^+\mu^-)$, $2(\tau^+\tau^-)$,
$e^+e^-\mu^+\mu^-$, $e^+e^-\tau^+\tau^-$, \ldots) at lowest order in QED. In
contrast to the case of vector meson decay into a single pair of leptons, the
lepton mass must be retained in these four-lepton decay channels to cutoff the
mass singularity. Owing to more pronounced collinear enhancement, the branching
fractions of vector mesons decays into $ 2(e^+e^-)$ are considerably greater
than those for decays into $2(\mu^+\mu^-)$. The decay channels
$J/\psi(\Upsilon)\to 2(e^+e^-), e^+e^-\mu^+\mu^-$ are predicted to have
branching fractions of order $10^{-5}$, which appear to have bright observation
prospect at {\tt BESIII}, {\tt Belle 2} and {\tt LHC} experiments.
