  We discuss the cosmological gravitino problem in inflation models in which
the inflaton potential is constructed from K\"ahler potential rather than
superpotential: a representative model is $\overline{\text{D}3}$-induced
geometric inflation. A critical ingredient in this type of models is the
coupling of the inflaton and Polonyi (supersymmetry-breaking) field in the
K\"ahler potential, which is needed to build the inflaton potential. We point
out the same coupling let the inflaton dominantly decay into a pair of
inflatino and gravitino causing the gravitino problem. We propose some possible
solutions to this problem.
