  The semi-constrained NMSSM (scNMSSM) extends the MSSM by a singlet field, and
requires unification of the soft SUSY breaking terms in the squark and slepton
sectors, while it allows that in the Higgs sector to be different. We try to
interpret the muon g-2 in the scNMSSM, under the constraints of 125 GeV Higgs
data, B physics, searches for low and high mass resonances, searches for SUSY
particles at the LHC, dark matter relic density by WMAP/Planck, and direct
searches for dark matter by LUX, XENON1T, and PandaX-II. We find that under the
above constraints, the scNMSSM can still (i) satisfy muon g-2 at 1$\sigma$
level, with a light muon sneutrino and light chargino; (ii) predict a
highly-singlet-dominated 95~GeV Higgs, with a diphoton rate as hinted at by CMS
data, because of a light higgsino-like chargino and moderate $\lambda$; (iii)
get low fine tuning from the GUT scale with small $\mu_{\rm eff},\, M_0,\,
M_{1/2},\, {\rm and}\, A_0$, with a lighter stop mass which can be as low as
about 500 GeV, which can be further checked in future studies with search
results from the 13~TeV LHC; (iv) have the lightest neutralino be
singlino-dominated or higgsino-dominated, while the bino and wino are heavier
because of high gluino bounds at the LHC and universal gaugino conditions at
the GUT scale; (v) satisfy all the above constraints, although it is not easy
for the lightest neutralino, as the only dark matter candidate, to get enough
relic density. Several ways to increase relic density are discussed.
