  A new U(1) gauge symmetry is the simplest extension of the Standard Model and
has various theoretical and phenomenological motivations. In this paper, we
study the cosmological constraint on the MeV scale dark photon. After the
neutrino decoupling era at $T = \mathcal{O}(1)\,$MeV, the decay and
annihilation of the dark photon heats up the electron and photon plasma and
accordingly decreases the effective number of neutrino $N_{\mathrm{eff}}$ in
the recombination era. We derive a conservative lower-limit of the dark photon
mass around 8.5 MeV from the current Planck data if the mixing between the dark
photon and ordinary photon is larger than $\mathcal{O}(10^{-9})$. We also find
that the future CMB stage-$\rm I\! V$ experiments can probe up to 17 MeV dark
photon.
