  We discuss the possibility of producing a light dark photon dark matter
through a coupling between the dark photon field and the inflaton. The dark
photon with a large wavelength is efficiently produced due to the inflaton
motion during inflation and becomes non-relativistic before the time of
matter-radiation equality. We compute the amount of production analytically.
The correct relic abundance is realized with a dark photon mass extending down
to $10^{-21} \, \rm eV$.
