  We investigate the instanton effect due to D3 branes wrapping a four-cycle in
a Calabi-Yau orientifold with D7 branes. We study the condition for the nonzero
superpotentials from the D3 instantons. For that matter we work out the zero
mode structures of D3 branes wrapping a four-cycle both in the presence of the
fluxes and in the absence of the fluxes. In the presence of the fluxes, the
condition for the nonzero superpotential could be different from that without
the fluxes. We explicitly work out a simple example of the orientifold of $K3
\times T^2/Z_2$ with a suitable flux to show such behavior. The effects of
D3-D7 sectors are interesting and give further constraints for the nonzero
superpotential. In a special configuration where D3 branes and D7 branes wrap
the same four-cycle, multi-instanton calculus of D3 branes could be reduced to
that of a suitable field theory. The structure of D5 instantons in Type I
theory is briefly discussed.
