  Very recently, the Fermilab report of muon $(g-2)$ shows a $4.2\sigma$
discrepancy between the standard model prediction. Motivated by this inspiring
result and the strengthening tension with the dark matter observations. We
argue that in general next-to-minimal supersymmetric standard model, a
singlino-dominated neutralino and singlet-dominated Higgs bosons may form a
secluded dark matter sector with $\tilde{\chi}_1^0\tilde{\chi}_1^0 \to h_s A_s$
responsible for the measured abundance by adopting an appropriate Yukawa
coupling $\kappa$. This sector communicates with the Standard Model sector by a
weak singlet-doublet Higgs mixing. So the scatterings of the singlino-dominated
dark matter with nucleons are suppressed. Besides, the dark matter must be
heavier than about $160~{\rm GeV}$ to proceed with the annihilation, sparticle
decay chains are lengthened in comparison with the minimal supersymmetric
standard model prediction due to the singlet nature of the dark matter, and the
singlet-dominated Higgs bosons as final state usually increase sparticle decay
channel. These characteristics make sparticle detection at LHC rather tricky.
This study shows that the theory can readily explain the discrepancy of the
muon anomalous magnetic moment between its SM prediction and experimentally
measured value, without conflicting the DM and the Higgs experimental results
and the LHC searches for sparticle.
