  We study the phenomenology of the Peccei-Quinn invariant extension of the
next-to-minimal supersymmetric standard model (NMSSM) in view of the recent
discovery of a 125 GeV Higgs boson. The minimal model having no quadratic and
cubic terms of the NMSSM singlet field predicts a light singlino-like lightest
supersymmetric particle (LSP). The model is strongly constrained by the Higgs
invisible decay and the dark matter characteristic of the LSP, while some
constraints can be relaxed by assuming that the saxion, the CP-even companion
of the axion in the Peccei-Quinn sector, causes a late-time entropy production
diluting the thermal LSP density. The collider signal of the model contains
multi-jet and $h/W/Z$ plus missing energy, which can be discovered in the early
stage of the 14 TeV LHC running.
