  We study a Peccei-Quinn invariant extension of the next-to-minimal
supersymmetric Standard Model (NMSSM), which turns out to be free from the
tadpole and domain wall problems. Having a non-renormalizable coupling to the
axion superfield, the SM singlet added to the Higgs sector can naturally
generate an effective Higgs mu term around the weak scale. In the model, the
lightest neutralino is dominated by the singlino, which gets a mass only
through mixing with the neutral Higgsinos. We explore the phenomenological
consequences resulting from the existence of such a relatively light
neutralino. The coupling of the SM singlet to the Higgs doublets is constrained
by the experimental bound on the invisible Z-boson decay width. Under this
constraint, we examine the properties of the SM-like Higgs boson paying
attention to its mass and decays. We also demonstrate a UV completion of the
model in SU(5) grand unified theory with a missing-partner mechanism.
