  Under current LHC and dark matter constraints, the general NMSSM can have
self-interacting dark matter to explain the cosmological small structure. In
this scenario, the dark matter is the light singlino-like neutralino ($\chi$)
which self-interacts through exchanging the light singlet-like scalars ($h_1,
a_1$). These light scalars and neutralinos inevitably interact with the 125 GeV
SM-like Higgs boson ($h_{SM}$), which cause the Higgs exotic decays $h_{SM} \to
h_1 h_1, a_1 a_1, \chi\chi$. We first demonstrate the parameter space required
by the explanation of the cosmological small structure and then display the
Higgs exotic decays. We find that in such a parameter space the Higgs exotic
decays can have branching ratios of a few percent, which should be accessible
in the future $e^+e^-$ colliders.
