  We propose a model of bimetric gravity in which the mixing of metrics
naturally gives a mass to a graviton by the compactification with flux of two
gauge fields in extra dimensions. We assume that each metric in the solution
for the background geometry describes the four-dimensional Minkowski spacetime
with an $S^2$ extra space, though the two radii of $S^2$ for two metrics take
different values in general. The solution is derived by the effective potential
method in the presence of the magnetic fluxes on the extra spheres. We find
that the a massive graviton is governed by the Fierz-Pauli Lagrangian in the
weak field limit and one massless graviton left in four dimensions.
