We study the effects of D-brane instantons wrapping rigid cycles on the Z(2) x Z(2)' toroidal orbifold. We compute Majorana masses induced by rigid D-brane instantons and realize bimaximal mixing matrices in certain models. We can also derive more generic mass matrices in other models. The bimaximal mixing Majorana mass matrix provides a possibility for explaining observed mixing angles. We also compute the mu-term matrix among more than one pair of Higgs fields induced by rigid D-brane instantons.