  The next-to-minimal supersymmetric model (NMSSM) with a large lambda (the
mixing parameter between the singlet and doublet Higgs fields) is well
motivated since it can significantly push up the upper bound on the SM-like
Higgs boson mass to solve the little hierarchy problem. In this work we examine
the current experimental constraints on the NMSSM with a large lambda, which
include the direct search for Higgs boson and sparticles at colliders, the
indirect constraints from precision electroweak measurements, the cosmic dark
matter relic density, the muon anomalous magnetic moment, as well as the
stability of the Higgs potential. We find that, with the increase of lambda,
parameters like tan-beta, M_A, mu and M_2 are becoming more stringently
constrained. It turns out that the maximal reach of lambda is limited by the
muon anomalous magnetic moment, and for smuon masses of 200 GeV (500 GeV) the
parameter space with lambda > 1.5 (0.6) is excluded.
