  We study the \mu \to e \gamma decay in the Z_3-invariant next-to-minimal
supersymmetric (SUSY) Standard Model (NMSSM) with superheavy right-handed
neutrinos. We assume that the soft SUSY breaking parameters are generated at
the GUT scale, not universally as in the minimal supergravity scenario but in
such a way that those soft parameters which are specific to the NMSSM can
differ from the soft parameters which involve only the MSSM fields while
keeping the universality at the GUT scale within the soft parameters for the
MSSM and right-handed neutrino fields. We call this type of boundary conditions
"semi-constrained". In this model, the lepton-flavor-violating off-diagonal
elements of the slepton mass matrix are induced by radiative corrections from
the neutrino Yukawa couplings, just like as in the MSSM extended with the
right-handed neutrinos, and these off-diagonal elements induce sizable rates of
\mu \to e \gamma depending on the parameter space. Since this model has more
free parameters than the MSSM, the parameter region favored from the Higgs
boson mass can slightly differ from that in the MSSM. We show that there is a
parameter region in which the \mu \to e \gamma decay can be observable in the
near future even if the SUSY mass scale is about 4 TeV.
