  The observation of a protophobic 16.7 MeV vector boson has been reported by a
$^8$Be nuclear transition experiment. Such a new particle could mediate between
the Standard Model and a dark sector, which includes the dark matter. In this
paper, we show some simple models of the dark matter which satisfy the thermal
relic abundance under the current experimental bounds from the direct and the
indirect detections. In a model, it is found that an appropriate
self-scattering cross section to solve the small scale structure puzzles can be
achieved.
