  In the semi-constrained NMSSM (scNMSSM, or NMSSM with non-universal Higgs
mass) under current constraints, we consider a scenario where $h_2$ is the
SM-like Higgs, $\tilde{\chi}^0_1$ is singlino-dominated LSP,
$\tilde{\chi}^{\pm}_1$ and $\tilde{\chi}^0_{2,3}$ are mass-degenerated, light
and higgsino-dominated NLSPs (next-to-lightest supersymmetric particles). We
investigate the constraints to these NLSPs from searching for SUSY particles at
the LHC Run-I and Run-II, discuss the possibility of discovering these NLSPs in
the future, and come to the following conclusions: (i) With all data of Run I
and up to 36 $\rm fb^{-1}$ data of Run II at the LHC, the search results by
ATLAS and CMS can still not exclude the higgsino-dominated NLSPs of
$100\sim200$ GeV. (ii) When the mass difference with $\tilde{\chi}^0_{1}$ is
smaller than $m_{h_2}$, $\tilde{\chi}^0_{2}$ and $\tilde{\chi}^0_{3}$ have
opposite preference on decaying to $Z/Z^*$ or $h_1$. (iii) When the mass
difference between NLSP and LSP is larger than $m_Z$, most of the samples can
be checked at $5\sigma$ level with future 300 $\rm fb^{-1}$ data at the LHC.
While with 3000 $\rm fb^{-1}$ data at the High Luminosity LHC (HL-LHC), nearly
all of the samples can be checked at $5\sigma$ level even if the mass
difference is insufficient. (iv) The $a_1$ funnel and the $h_2/Z$ funnel
mechanisms for the singlino-dominated LSP annihilating can not be distinguished
by searching for NLSPs.
