  We consider a supersymmetric mirror Twin Higgs model in a gravity-mediated
supersymmetry-breaking scenario. We point out that the Polonyi field can be odd
under the $Z_{2}$ symmetry exchanging the Standard Model with the mirror sector
while gaugino masses are generated at tree-level. We discuss the dynamics of
the Polonyi field during and after inflation and show that the Polonyi problem
is absent. The Polonyi field couples to the two sectors with opposite signs,
which may serve as origin of the $Z_{2}$-breaking of the Higgs potential in
Twin Higgs models. We also estimate the $Z_2$-breaking in soft masses of
supersymmetric particles.
