  The slow-roll inflation is a beautiful paradigm, yet the inflaton potential
can hardly be sufficiently flat when unknown gravitational effects are taken
into account. However, the hybrid inflation models constructed in D = 4 N = 1
supergravity can be consistent with N = 2 supersymmetry, and can be naturally
embedded into string theory. This article discusses the gravitational effects
carefully in the string model, using D = 4 supergravity description. We adopt
the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2
orientifold for definiteness. It turns out that the slow-roll parameter can be
sufficiently small despite the non-minimal Kahler potential of the model. The
conditions for this to happen are clarified in terms of string vacua. We also
find that the geometry obtained by blowing up singularity, which is necessary
for the positive vacuum energy, is stabilized by introducing certain 3-form
fluxes.
