  We study K\"ahler moduli stabilizations in semi-realistic magnetized D-brane
models based on $ Z_2\times Z_2'$ toroidal orbifolds. In type IIB
compactifications, 3-form fluxes can stabilize the dilaton and complex
structure moduli fields, but there remain some massless closed string moduli
fields, K\"ahler moduli. The magnetic fluxes generate Fayet-Iliopoulos terms,
which can fix ratios of K\"ahler moduli. On top of that, we consider D-brane
instanton effects to stabilize them in concrete D-brane models and investigate
the brane configurations to confirm that the moduli fields can be stabilized
successfully. In this paper, we treat two types of D-brane models. One is based
on D9-brane systems respecting the Pati-Salam model. The other is realized in a
D7-brane system breaking the Pati-Salam gauge group. We find suitable
configurations where the D-brane instantons can stabilize the moduli fields
within both types of D-brane models, explaining an origin of a small constant
term of the superpotential which is a key ingredient for successful moduli
stabilizations.
