  By using a string-inspired modular invariant supergravity, which was proved
well to explain WMAP observations appropriately, a mechanism of supersymmetry
breaking (SSB) and Gravitino Production just after the end of inflation are
investigated. Supersymmetry is broken mainly by F-term of the inflaton
superfield and the Goldstino is identified to be inflatino in this model, which
fact is shown numerically. By using the canonically normalized and diagonalized
scalars, the decay rates of these fields are calculated, for both the $T$ and
$Y$ into gravitinos. Non-thermal production of gravitinos is not generated from
the inflaton (dilaton), since the inflaton mass is lighter than gravitino, but
they are produced by the decay of modular field $T$ and scalar field $Y$.
Because the reheating temperature $T_R$ is about order $\sim O(10^{10})$ GeV
and the mass of gravitino is $3.16 \times 10^{12}$ GeV, it is not reproduced
after the reheating of the universe. The gravitinos are produced almost
instantly just after the end of inflation through $Y$ and $T$, not from
inflaton. Because the decay time appears very rapid, gravitinos disappear
before the BBN stage of the universe. The effects of the lightest
supersymmetric particles (LSP) produced by gravitinos may be important to
investigate more carefully, if the LSP's are the candidate of dark matter.
