  In this paper, we consider radial standing waves to a nonlinear Klein-Gordon
equation with a repulsive inverse-square potential. It is known that existence
of a "radial" ground state to the stationary problem of the nonlinear
Klein-Gordon equation. Here, the "radial" ground state is a solution with the
least energy among radial solutions to the stationary problem. We deal with
stability and instability of the standing wave for the "radial" ground state.
